Device for calculating diffraction efficiencies of a diffraction lens, lens with grating element, and optical system for reading

ABSTRACT

A device for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, comprises a first memory for storing information about diffraction efficiencies of the regions; a second memory for storing information about weights corresponding to the regions; and a first processor for retrieving information from the first and the second memory, and calculating diffraction efficiencies of the entire diffraction lens using the formula                E   j     =       ∑     m   =   1     M            W   m          η   mj                 (   1   )                         
     wherein: 
     j: integer indicating the order of diffraction light 
     E j : diffraction efficiency for j-th order diffraction light of the diffraction lens 
     M: positive integer (M&gt;1) indicating the number of regions for which the diffraction efficiency is calculated 
     m: index of the region for which the diffraction efficiency is calculated 
     η mj : diffraction efficiency for the j-th order diffraction light of the m-th region (stored in the first memory) 
     W m : weight for the m-th region (stored in the second memory means). 
     Thus, the diffraction efficiency of the diffraction lens can be calculated easily.

FIELD OF THE INVENTION First Invention

The first invention relates to a diffraction lens (also referred to as“lens with grating element” or “lens with diffraction element” in thefollowing), in particular to a calculation (simulation) technique forcalculating a diffraction efficiency of a diffraction lens that is cutwith a diamond bit or molded using a die that is cut with a diamond bit,and a design technique for designing achromatic lenses.

Furthermore, the first invention relates to a lens with a gratingelement, particularly to a small size imaging apparatus such as a boardcamera or a monitoring camera etc. and a reading apparatus such as a barcode reader etc.

Second Invention

The second invention relates to an optical system for reading in whichchromatic aberration is excellently corrected, and to an image readingapparatus and a bar code reader using the same.

BACKGROUND OF THE INVENTION First Invention

In an optical system for imaging or an optical system for reading,imaging performance is of great importance. As factors that influencethe imaging performance, there are those inside the optical system suchas aberration of lenses, diffraction and dust, and those outside theoptical system such as environmental conditions. Particularly, chromaticaberration due to different refractive indices of a lens at differentwavelengths is one cause of deteriorating imaging performance.

Accordingly, conventional techniques try to reduce the chromaticaberration by combining several lenses having different Abbe numbers,and among other technologies, it is known that an anomalous dispersionglass may be used as an achromatic lens system.

Also, recently, as another technology for reducing chromatic aberration,a lens with diffraction element where a relief for providing diffractiveeffect is formed on a surface of the lens to correct chromaticaberration has been proposed. For example, in Publication of UnexaminedJapanese Patent Application (Tokuhyo) No. Hei 8-508116, it is proposedto correct chromatic aberration in the entire visible spectrum by asingle lens with diffraction element.

Recently, a large number of achromatic lenses and dual-focus lenses havebeen proposed where lens functionality is enhanced with diffractionlenses (see e.g. Publication of Unexamined Japanese Patent ApplicationNo. Hei 8-171052 and Japanese Patent Application No. Hei 8-290080). Mostof these diffraction lenses are so-called relief-type diffraction lenseshaving a periodic relief on a surface of a lens or flat plate of, forexample, glass.

There are basically two methods for forming a relief-type diffractionlens. One method is to cut the lens with a diamond bit. In this case, asaw-tooth-shaped relief (relief profile) can be cut. The other methodinvolves photolithography and approximates this saw-tooth-shaped reliefwith a step relief. This is also called “binary method”.

Diffraction efficiencies are important parameters for the utilizationand the design of diffraction lenses.

It is widely known, that according to Swanson et al (G. J. Swanson andWilfrid B. Veldkamp, “Diffractive optical elements for use in infraredsystems”, Optical Engineering, Vol. 28, No. 6, (1989)), the relationbetween the number of masks used during manufacturing and thediffraction efficiency can be calculated for the binary method.

The retardation of the wave front passing a periodic relief-typediffraction grating with a grating ring interval (pitch) that issufficiently longer than the wavelength and a phase shift of about onewavelength can be calculated from the refractive index of the gratingmaterial on the basis of its cross-section. It is widely known (see e.g.M. C. Hutley, “Diffraction Grating”, Academic Press, Chap. 2, 1982) thatwhen the retardation is Fourier-transformed, the diffraction efficiencyof the diffraction grating can then be obtained as the Fouriercoefficients (scalar diffraction theory).

FIG. 49(a) outlines how a die for the diffraction lens is cut with adiamond bit. A die 1901, which rotates in the arrow direction, is cut bya diamond bit 1902. The diamond bit has a pointed tip, which is suitablefor cutting diffraction lenses or dies for diffraction lenses.

FIG. 49(b) is a magnification of FIG. 49(a) showing a cutting region A.The tip 1903 of the diamond bit describes a circular arc with a certaincurvature radius (nose radius) 1904. Even when the designed shape is asaw-tooth shape as indicated by the chain double-dashed line 1905, thedent left by the diamond bit is a circular arc 1906 that has almost thesame radius as the curvature radius of its tip.

FIG. 50 shows cross-sections outlining how a diffraction lens and a dieare cut. For the sake of simplicity, the diffraction lens is formed on aplanar substrate.

When the designed shape of the lens is as shown in FIG. 50(a), thedesigned shape of the die for manufacturing the lens is as shown in FIG.50(b). However, when the die is cut with a diamond bit 2001 whose tip isa circular arch with a certain curvature radius, the convex angularportions in the cross-section of the die will be rounded out, as shownin FIG. 50(c). As a result, lenses that are formed with that die have arelief profile as shown in FIG. 50(d).

FIG. 50(e) is a magnification of the cross-section shown in FIG. 50(c),showing the microscopic features of the cutting region A after thecutting. Depending on the feed speed and the curvature radius of thecutting bit, cutting traces 2002 amounting to a tiny undulation remainon the cut surface. These cutting traces are transferred to the lenssurface.

Since the diffraction efficiency of the diffraction lens is influencedby the relief profile, it may turn out to be quite different from thedesigned value, if the relief profile degenerates like this during themanufacturing step.

As mentioned above, the cutting bit can have a pointed tip to avoid achange of the diffraction efficiency, but then, many technicallydifficult problems arise. For example, the necessary cutting distancebecomes long, the degeneration due to abrasion of the cutting bitbecomes large, and the cutting bit chips more easily. As a result, theproductivity becomes considerably worse.

If the relationship between the curvature radius of the cutting bit andthe diffraction efficiency of the obtained diffraction lens were known,it could be decided before the cutting process which cutting bit shouldbe chosen to keep the decrease in diffraction efficiency during themanufacturing process in a tolerable range, and the used bit would nothave to be sharper than necessary, which would be very useful for theproduction efficiency.

If, at the design stage, the diffraction efficiency of the lens could becalculated with consideration to the processing method, then theprocessing method could be taken into account as one of the lens designparameters and lenses that are easier to manufacture could be designed.Consequently, there is a need for an easy calculation method forcalculating, at the design stage, the finally attained diffractionefficiency with consideration to the processing method.

A typical example of an application for a diffraction lens is the use asan achromatic lens to correct the chromatic aberration of a refractivelens with the chromatic aberration of the diffraction lens. Such lensesare known, for example from Publications of Unexamined Japanese PatentPublication No. Hei 6-242373 and No. Hei 8-171052. In the lensesdisclosed in both of these publications, the number of grating rings islarge, so that it is difficult to cut a die for the lens using, forexample, a diamond bit. Moreover, the diffraction efficiency candecrease due to deterioration of the shape because of the curvature atthe vertex of the cutting bit. In the above publications, these problemswere not addressed by the design considerations, so that it wasdifficult to ensure both diffraction efficiency and productivity.

Furthermore, in the above-mentioned conventional technologies, thepitches of the relief rings that form a grating element graduallydecrease with increasing distance from the optical axis. Thus, the pitchbecomes very small at the peripheral portion, so that problems such asdecreased diffraction efficiency or processing difficulties may result.

Also, if lateral chromatic aberration (magnification chromaticaberration) of a wide-angle lens having a half field angle of at least60° is to be corrected with a single grating element surface, the focallength of the grating element must be short. However, in such acondition, longitudinal chromatic aberration (axial chromaticaberration) is excessively corrected, so that good imaging performancecannot be obtained. Furthermore, because the number of the relief ringsalso increases, problems such as decrease in diffraction efficiency ordifficulty in processing may be caused.

Second Invention

Various optical systems for reading that form images from imageinformation, or manuscript or code information etc. on an image sensorsuch as a charge-coupled device (CCD) have been proposed. It is requiredthat such optical systems for reading should have modulation transferfunction (MTF) that is high enough to project a manuscript on a CCD linesensor having high density, so that satisfactory correction of variousaberrations is needed.

Conventionally, particularly in order to correct chromatic aberration asa cause of deterioration in imaging performance, combinations ofmultiple lenses with different Abbe numbers have been used. For example,in Publication of Unexamined Japanese Patent Application (Tokukai) No.Hei 5-119255, a technology that intends to correct chromatic aberrationby forming an optical system for reading using three lenses in threegroups, and also to enable low-cost production by using plasticmaterials as a lens material is disclosed. Furthermore, in Publicationof Unexamined Japanese Patent Application (Tokukai) No. Hei 5-135193, abar code reader, in which the optical system for reading is formed byusing a single aspheric lens, is disclosed.

However, in the optical system for reading as disclosed in theabove-mentioned Publication of Unexamined Japanese Patent Application(Tokukai) No. Hei 5-119255, due to the need for multiple lenses,low-cost production is limited in view of processing and assembly of thelenses. Furthermore, although it is intended to achieve low-costproduction by using plastic materials for the lens materials, becausetypes of plastic materials are limited, correction of chromaticaberration is also restricted. Also, in the bar code reader disclosed inthe above-mentioned Publication of Unexamined Japanese PatentApplication (Tokukai) No. Hei 5-135193, because chromatic aberrationcannot be corrected and a single wavelength is required, a light sourcesuch as an LED is needed, thus limiting miniaturization and low-costproduction.

SUMMARY OF THE INVENTION

To solve the above problems, it is an object of the first presentinvention to provide a simple method for calculating the diffractionefficiency of a lens molded with a die that was cut with a diamond bit.

It is another object of the first present invention to provide acombined refraction/diffraction lens that can be cut with highproductivity using a diamond bit and which provides sufficientachromatism.

Furthermore, an object of the first invention is to solve theabove-mentioned problems, and to provide a lens with a diffractionelement that can be processed easily while utilizing the characteristicsof conventional lenses with diffraction elements by devising the pitchesof the relief rings which provide diffractive effect.

An object of the second invention is to solve the above-mentionedproblems in conventional technologies, and provide an optical system forreading in which chromatic aberration is corrected without increasingthe number of lens components and by which good imaging performance canbe attained, and an image reading apparatus and a bar code reader usingthe same, by providing a surface of the lens with diffractive effect.

First Invention

In accordance with a first configuration of the present invention, adevice for calculating diffraction efficiencies of a diffraction lensdivided into a plurality of regions, each region comprising at least onegrating ring, comprises:

a first memory for storing information about diffraction efficiencies ofthe regions;

a second memory for storing information about weights corresponding tothe regions;

a first processor for retrieving information from the first and thesecond memory, and calculating diffraction efficiencies of the entirediffraction lens in accordance with the formula $\begin{matrix}{E_{j} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mj}}}} & (1)\end{matrix}$

 wherein:

j: integer indicating the order of diffraction light

E_(j): diffraction efficiency for j-th order diffraction light of thediffraction lens

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m: index of the region for which the diffraction efficiency iscalculated

η_(mj): diffraction efficiency for the j-th order diffraction light ofthe m-th region (stored in the first memory)

W_(m): weight for the m-th region (stored in the second memory means).

In accordance with the first configuration of the present invention, amethod for calculating diffraction efficiencies of a diffraction lensdivided into a plurality of regions, each region comprising at least onegrating ring, comprises:

a first memory step of storing information about diffractionefficiencies of the regions;

a second memory step of storing information about weights correspondingto the regions;

a first processing step of retrieving information stored in the firstand the second memory step, and calculating diffraction efficiencies ofthe entire diffraction lens in accordance with the formula$\begin{matrix}{E_{j} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mj}}}} & (1)\end{matrix}$

 wherein:

j: integer indicating the order of diffraction light

E_(j): diffraction efficiency for j-th order diffraction light of thediffraction lens

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m : index of the region for which the diffraction efficiency iscalculated

ηm_(j): diffraction efficiency for the j-th order diffraction light ofthe m-th region (stored in the first memory step)

W_(m): weight for the m-th region (stored in the second memory step).

In accordance with the first configuration of the present invention, acomputer-readable recording medium stores a computer-executable programfor calculating diffraction efficiencies of a diffraction lens dividedinto a plurality of regions, each region comprising at least one gratingring, which program executes:

a first memory step of storing information about diffractionefficiencies of the regions;

a second memory step of storing information about weights correspondingto the regions; and

a first processing step of retrieving information stored in the firstand the second memory step, and calculating diffraction efficiencies ofthe entire diffraction lens in accordance with the formula$\begin{matrix}{E_{j} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mj}}}} & (1)\end{matrix}$

 wherein:

j: integer indicating the order of diffraction light

E_(j): diffraction efficiency for j-th order diffraction light of thediffraction lens

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m: index of the region for which the diffraction efficiency iscalculated

η_(mj): diffraction efficiency for the j-th order diffraction light ofthe m-th region (stored in the first memory step)

W_(m): weight for the m-th region (stored in the second memory step).

In accordance with this first configuration of the present invention,the diffraction lens is divided into a plurality of regions, and aweight is assigned to each region to determine the diffractionefficiency of the entire lens, so that the diffraction efficiency of theentire lens can be calculated precisely and efficiently, even when theregions have different diffraction efficiencies. It is preferable thatthe calculation of diffraction efficiencies according to the presentinvention is performed on a computer.

In accordance with a second configuration of the present invention, adevice for calculating diffraction efficiencies of a diffraction lensdivided into a plurality of regions, each region comprising at least onegrating ring, the diffraction efficiencies corresponding to a pluralityof wavelengths, comprises:

a first memory for storing information about diffraction efficiencies ofthe regions at the plurality of wavelengths;

a second memory for storing information about weights corresponding tothe regions;

a third memory for storing information about a relief cross-sectionshape of the diffraction lens;

a fourth memory for storing information about the plurality ofwavelengths;

a fifth memory for storing information about refractive indices of amaterial of the diffraction lens at the wavelengths;

a fourth processor for calculating a relief cross-section shape of thediffraction lens stored in the third memory;

a second processor for retrieving information from the third, fourth andfifth memory, and calculating therefrom diffraction efficiencies of theregions at the plurality of wavelengths stored in the first memory;

a third repeating means for operating the second processor for a numberof times that is equal to the number of the wavelengths;

a fourth repeating means for operating the third repeating means for anumber of times that is equal to the number of the regions; and

a first processor for retrieving information from the first and thesecond memory, and calculating diffraction efficiencies of the entirediffraction lens using the formula $\begin{matrix}{E_{jl} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mjl}}}} & (5)\end{matrix}$

 wherein:

j: integer indicating the order of diffraction light

l: index of the wavelengths

E_(jl): diffraction efficiency for j-th order diffraction light of thediffraction lens at the l-th wavelength

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m: index of the region for which the diffraction efficiency iscalculated

W_(m): weight for the m-th region

η_(mjl): diffraction efficiency for the j-th order diffraction light ofthe m-th region at the l-th wavelength

In accordance with the second configuration of the present invention, amethod for calculating diffraction efficiencies of a diffraction lensdivided into a plurality of regions, each region comprising at least onegrating ring, the diffraction efficiencies corresponding to a pluralityof wavelengths, comprises:

a first memory step of storing information about diffractionefficiencies of the regions at the plurality of wavelengths;

a second memory step of storing information about weights correspondingto the regions;

a third memory step of storing information about a relief cross-sectionshape of the diffraction lens;

a fourth memory step of storing information about the plurality ofwavelengths;

a fifth memory step of storing information about refractive indices of amaterial of the diffraction lens at the wavelengths;

a fourth processing step of calculating a relief cross-section shape ofthe diffraction lens stored in the third memory step;

a second processing step of retrieving information stored in the third,fourth and fifth memory step, and calculating therefrom diffractionefficiencies of the regions at the plurality of wavelengths stored inthe first memory step;

a third repeating step of repeating the second processing step for anumber of times that is equal to the number of the wavelengths;

a fourth repeating step of repeating the third repeating step for anumber of times that is equal to the number of the regions; and

a first processing step of retrieving information stored in the firstand the second memory step, and calculating diffraction efficiencies ofthe entire diffraction lens using the formula $\begin{matrix}{E_{jl} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mjl}}}} & (5)\end{matrix}$

 wherein:

j: integer indicating the order of diffraction light

l: index of the wavelengths

E_(jl): diffraction efficiency for j-th order diffraction light of thediffraction lens at the l-th wavelength

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m: index of the region for which the diffraction efficiency iscalculated

W_(m): weight for the m-th region

η_(mjl): diffraction efficiency for the j-th order diffraction light ofthe m-th region at the l-th wavelength.

In accordance with the second configuration of the present invention, acomputer-readable recording medium stores a computer-executable programfor calculating diffraction efficiencies of a diffraction lens dividedinto a plurality of regions, each region comprising at least one gratingring, the diffraction efficiencies corresponding to a plurality ofwavelengths, wherein the program executes:

a first memory step of storing information about diffractionefficiencies of the regions at the plurality of wavelengths;

a second memory step of storing information about weights correspondingto the regions;

a third memory step of storing information about a relief cross-sectionshape of the diffraction lens;

a fourth memory step of storing information about the plurality ofwavelengths;

a fifth memory step of storing information about refractive indices of amaterial of the diffraction lens at the wavelengths;

a fourth processing step of calculating a relief cross-section shape ofthe diffraction lens stored in the third memory step;

a second processing step of retrieving information stored in the third,fourth and fifth memory step, and calculating therefrom diffractionefficiencies of the regions at the plurality of wavelengths stored inthe first memory step;

a third repeating step of repeating the second processing step for anumber of times that is equal to the number of the wavelengths;

a fourth repeating step of repeating the third repeating step for anumber of times that is equal to the number of the regions; and

a first processing step of retrieving information stored in the firstand the second memory step, and calculating diffraction efficiencies ofthe entire diffraction lens using the formula $\begin{matrix}{E_{jl} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mjl}}}} & (5)\end{matrix}$

 wherein:

j: integer indicating the order of diffraction light

l: index of the wavelengths

E_(jl): diffraction efficiency for j-th order diffraction light of thediffraction lens at the l-th wavelength

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m: index of the region for which the diffraction efficiency iscalculated

W_(m): weight for the m-th region

η_(mjl): diffraction efficiency for the j-th order diffraction light ofthe m-th region at the l-th wavelength.

In accordance with this second configuration of the present invention,the diffraction efficiencies at a plurality of wavelengths can becalculated with comparatively little memory and high speed.

According to the present invention, a lens-shape measurement apparatusfor measuring the surface shape of a measurement object selected fromthe group consisting of a diffraction lens and a die for a diffractionlens comprises:

a shape measuring means for measuring the surface shape of themeasurement object;

a processor device for substantially eliminating at least one of themacroscopic components selected from the group consisting of a sphericalsurface, an aspherical surface, and a plane from measurement dataobtained with the shape measuring means; and

a device for calculating diffraction efficiencies of the diffractionlens based on the measured data from which the macroscopic component hasbeen substantially eliminated;

wherein the device for calculating diffraction efficiencies is a deviceaccording to the first configuration of the present invention.

According to the present invention, a method for calculating diffractionefficiencies of a diffraction lens by measuring the surface shape of ameasurement object selected from the group consisting of a diffractionlens and a die for a diffraction lens, comprises:

a shape measuring step of measuring the surface shape of the measurementobject;

a processing step of substantially eliminating at least one of themacroscopic components selected from the group consisting of a sphericalsurface, an aspherical surface, and a plane from measurement dataobtained in the shape measuring step; and

a step of calculating diffraction efficiencies of the diffraction lensbased on the measured data from which the macroscopic component has beensubstantially eliminated;

wherein the step of calculating diffraction efficiencies is a methodaccording to the first configuration of the present invention.

According to the present invention, a computer-readable recording mediumstores a computer-executable program for calculating diffractionefficiencies of a diffraction lens by measuring the surface shape of ameasurement object selected from the group consisting of a diffractionlens and a die for a diffraction lens, wherein the program executes:

a shape measuring step of measuring the surface shape of the measurementobject;

a processing step of substantially eliminating at least one of themacroscopic components selected from the group consisting of a sphericalsurface, an aspherical surface, and a plane from measurement dataobtained in the shape measuring step; and

a step of calculating diffraction efficiencies of the diffraction lensbased on the measured data from which the macroscopic component has beensubstantially eliminated;

wherein the program for executing the step of calculating diffractionefficiencies is a program stored in a recording medium according to thefirst configuration of the present invention.

In accordance with this configuration, the diffraction efficiencies ofdiffraction lenses can be obtained by measuring relief profiles ofactually obtained diffraction lenses or dies for molding diffractionlenses, so that it can be determined to what extent the precision of theobtained lens or the obtained die for molding lenses influences thediffraction efficiency. Thus, useful validation data for quality controlsuch as precision tolerances or discrimination of faulty articles can beobtained. Moreover, by comparing diffraction efficiencies calculatedfrom the actually obtained relief profile to diffraction efficiencies asdetermined from the design of a relief profile, the relation between theprocessing conditions for manufacturing a diffraction lens and thediffraction efficiency of the obtained lens can be determined.Consequently, this relation can be considered in the lens design, sothat a precise prediction of the diffraction efficiency of the finallyobtained diffraction lens and the selection of optimum manufacturingconditions become possible.

According to the present invention, an apparatus for designingdiffraction lenses comprises:

an input for entering lens design data; and

a processor for calculating optical properties and diffractionefficiencies of the diffraction lens obtained on the basis of the designdata;

wherein the processor for calculating the diffraction efficiencies is adevice for calculating diffraction efficiencies according to the firstconfiguration of the present invention.

According to the present invention, a method for designing diffractionlenses, comprises:

an input step of entering lens design data;

a processing step of calculating optical properties and diffractionefficiencies of the diffraction lens obtained on the basis of the designdata;

an optimization step of optimizing the lens properties based on theresult of the processing step;

wherein the processing step of calculating the diffraction efficienciesis a method for calculating diffraction efficiencies according to thefirst configuration of the present invention.

According to the present invention, a computer-readable recording mediumstores a computer-executable program for designing a diffraction lens,and executing on a computer an evaluation function for evaluating lensproperties; wherein the recording medium is in accordance with the firstconfiguration of the present invention.

In accordance with this configuration, the optical properties anddiffraction efficiencies of diffraction lenses obtained on the basis ofdesign data can be predicted precisely, so that the lenses can bedesigned in consideration of restrictions due to both correction ofchromatic aberration and tolerances of the diffraction efficiencies.Consequently, diffraction lenses with excellent characteristics can bedesigned in a short time and with high efficiency. Moreover, taking theconditions for the lens manufacturing process (for example the curvatureradius of the tip of the cutting bit or the feed speed of the cuttingbit) and their relation to the diffraction efficiency of the resultinglens into account, optimum manufacturing conditions can be determined atthe time of lens design.

In accordance with the present invention, a combinedrefraction/diffraction lens comprises a refraction lens; and adiffraction lens comprising a plurality of concentric grating ringsformed on at least one surface of the refraction lens; and satisfies theformula $\begin{matrix}{{k = {f\left( {\frac{1}{f_{g}} + \frac{v_{g}}{f_{d}v_{d}}} \right)}},} & (6)\end{matrix}$

wherein:

f: total focal length of the combined refraction/diffraction lens

f_(d): focal length of the diffraction lens

f_(g): focal length of the refraction lens

ν_(d): partial dispersion coefficient at an applied wavelength region ofthe diffraction lens

ν_(g): partial dispersion coefficient at an applied wavelength region ofthe refraction lens

wherein k satisfies 0.1≦k.

In accordance with this configuration, combined refraction/diffractionlenses and dies for molding combined refraction/diffraction lenses,which are cut with a diamond bit, can be manufactured with highproductivity.

In accordance with the present invention, a combinedrefraction/diffraction objective lens for use in an optical informationrecording/reproducing device comprises:

a single lens having an ingoing surface and an outgoing surface; and

a diffraction lens comprising a plurality of concentric grating ringsformed on at least one surface of the single lens;

and satisfies the formula $\begin{matrix}{{k = {f\left( {\frac{1}{f_{g}} + \frac{v_{g}}{f_{d}v_{d}}} \right)}},} & (6)\end{matrix}$

 wherein:

f: total focal length of the combined refraction/diffraction lens

f_(d): focal length of the diffraction lens

f_(g): focal length of the refraction lens

ν_(d): partial dispersion coefficient at an applied wavelength region ofthe diffraction lens

ν_(g): partial dispersion coefficient at an applied wavelength region ofthe refraction lens

ν_(g): partial dispersion coefficient at an applied wavelength region ofthe refraction lens

 wherein k satisfies 0.2≦k≦0.6.

In accordance with this configuration, combined refraction/diffractionobjective lenses and dies for molding combined refraction/diffractionobjective lenses, which are cut with a diamond bit, can be manufacturedwith good chromatic aberration correction and high productivity.Consequently, an optical head including an objective lens according tothe present invention can attain excellent signal output, because thefocal length of the objective lens varies only little when thewavelength of the light source varies, and stray light can be reduced.Moreover, the optical heads comprising a single objective lens with suchproperties can be devised significantly smaller.

According to the present invention, a combined refraction/diffractionimaging lens comprises:

a single lens having an ingoing surface and an outgoing surface; and

a diffraction lens comprising a plurality of concentric grating ringsformed on at least one surface of the single lens;

satisfying the formula $\begin{matrix}{{k = {f\left( {\frac{1}{f_{g}} + \frac{v_{g}}{f_{d}v_{d}}} \right)}},} & (6)\end{matrix}$

 wherein:

f: total focal length of the combined refraction/diffraction lens

f_(d): focal length of the diffraction lens

f_(g): focal length of the refraction lens

ν_(d): partial dispersion coefficient at an applied wavelength region ofthe diffraction lens

ν_(g): partial dispersion coefficient at an applied wavelength region ofthe refraction lens

ν_(g): partial dispersion coefficient at an applied wavelength region ofthe refraction lens

 wherein k satisfies 0.3≦k.

In accordance with this configuration, imaging lenses and dies formolding imaging lenses, which are cut with a diamond bit, can bemanufactured with high productivity. Moreover, if 0.4≦k≦0.7, thenprocessability is excellent, and an imaging lens with good resolutioncan be obtained. Consequently, an image pickup device comprising animaging lens according to the present invention can attain a picturewith little flare and excellent elimination of achromatic aberration.

Furthermore, in order to attain the above-mentioned objects, a lens witha grating element in accordance with the first configuration of thepresent invention is characterized by that, in the lens with a gratingelement in which chromatic aberration is corrected by forming concentricrelief rings on a surface of the lens to provide diffractive effect, thepitch P_(m) of the relief rings satisfies the formula $\begin{matrix}{{P_{m} > \sqrt{\frac{\lambda_{1} \cdot f_{d}}{2m}}},} & (7)\end{matrix}$

where m is the ring number counted from the center of the lens, f_(d) isthe focal length of the grating element, and λ₁ is the principalwavelength of the grating element.

By satisfying Formula (7), a grating element surface can easily beproduced. In addition, decrease in diffraction efficiency can beprevented, so that influence of unnecessary scattered light beingprojected on an image surface to decrease the imaging performance can beinhibited.

A lens with a grating element in accordance with the secondconfiguration of the present invention is characterized by that, in thelens with a grating element in which chromatic aberration is correctedby forming concentric relief rings on a surface of the lens to providediffractive effect, the itches of the relief rings gradually decrease toa certain position away from the optical axis, and gradually increasefurther away from the position.

By using such a configuration, the grating element surface can easily beproduced, while function of excellent correction of chromatic aberrationis maintained. Furthermore, decrease in diffraction efficiency can beprevented, so that influence of unnecessary scattered light beingprojected on an image surface to decrease the imaging performance can beinhibited.

A lens with a grating element in accordance with the third configurationof the present invention is characterized by that, in the lens with agrating element in which chromatic aberration is corrected by formingconcentric relief rings on a surface of the lens to provide diffractiveeffect, the following Formula (8) is satisfied: $\begin{matrix}{0.2 < {\frac{d}{r}} < 0.7} & (8)\end{matrix}$

where r is the effective radius of the grating element surface, and d isthe distance of the innermost ring of the relief from the optical axis.

By using such a configuration, a lens shape particularly useful forcorrecting lateral chromatic aberration can be obtained, and excessivecorrection of longitudinal chromatic aberration can also be inhibited.

Furthermore, in the lens with a grating element in accordance with thefirst to third configurations of the present invention, it is preferablethat the grating element surface has a kinoform profile. Furthermore, itis preferable that the lens is made of glass or of plastic. By usingsuch a structure, a lens with a grating element having a kinoformprofile with excellent transcription performance can be achieved.

Furthermore, it is preferable that the lens with a grating element inaccordance with the first to third configurations of the presentinvention is formed from an infrared absorbing material. By using such amaterial, influence of unnecessary light in the infrared spectrumgenerated by the grating element surface being projected on an imagepickup device to decrease the imaging performance can be inhibited, sothat good imaging performance can be maintained.

Furthermore, in forming an imaging apparatus, it is preferable that theimaging apparatus comprises a lens with a grating element in accordancewith the first to third configurations of the present invention, animage pickup device and a signal processing circuit. By using such astructure, a small type imaging apparatus with very excellent imagingperformance can be obtained.

Furthermore, in forming a reading apparatus, it is preferable that thereading apparatus comprises a lens having grating element in accordancewith the first to third configurations of the present invention, animage sensor and a signal processing circuit. By using such a structure,a small type reading apparatus with very excellent imaging performancecan be obtained.

Second Invention

In order to attain the above-mentioned objects, the present inventionprovides an optical system for reading image information or codeinformation, which comprises a lens in which a grating element surfaceis formed on at least one surface of the lens. According to thisstructure, an optical system for reading with corrected chromaticaberration and having good imaging performance can be achieved.

Furthermore, it is preferable that the optical system for reading inaccordance with the present invention can be moved on the optical axisby a driving device. According to this preferable example, manuscriptshaving different sizes can be read, and also an optical system forreading with corrected chromatic aberration and good imaging performancecan be achieved.

Furthermore, in this preferable structure, it is preferable to satisfy

0.6<Y_(t)/Y_(W)<1  (14)

where Y_(W) is the maximum height of a manuscript when the opticalsystem for reading is moved closest to the object side, and Y_(t) is themaximum height of a manuscript when the optical system for reading ismoved closest to the image side.

According to this preferable example, a small size optical system forreading having good imaging performance can be achieved.

Furthermore, in the optical system for reading in accordance with thepresent invention, it is preferable that the lens that constitutes theoptical system for reading is only a single lens in which the gratingelement surface is formed, the image side surface of the lens being aconvex surface and having a positive refractive power, and a diaphragmbeing placed on the object side from the lens. According to thispreferable example, a low-priced optical system for reading with goodimaging performance, in which chromatic aberration is corrected withoutincreasing the number of the lens components, can be achieved.

Furthermore, in this preferable structure, it is preferable to satisfy

0.05<|r₂/r₁|<0.5,  (9)

9<f/D<16,  (10)

and

0.05<|f/f_(d)|<0.15  (11)

where r₁ is the radius of curvature at the vertex of the object sidesurface of the lens, r₂ is the radius of curvature at the vertex of theimage side surface of the lens, D is the diameter of the diaphragm, f isthe focal length of the entire optical system, and f_(d) is the focallength of the grating element surface of the lens.

According to this preferable example, the following effects can beobtained. First, by satisfying Formula (9) above, an optimal lens shapein balance of various aberrations can be obtained. Then, by satisfyingFormula (10) above, sufficient depth of field to prevent loss of imageinformation or erroneous recognition of code information due tovibration etc. can be obtained. Then, by satisfying Formula (11) above,chromatic aberration can be excellently corrected.

In this case, it is further preferable that at least one surface of thelens is an aspheric surface with a local radius of curvature thatbecomes smaller with increasing distance from the optical axis.According to this preferable example, distortion aberration andcurvature of field can be corrected effectively.

Furthermore, in the optical system for reading in accordance with thepresent invention, it is preferable to satisfy

450 nm<λ₁<600 nm  (12)

where λ₁ is the principal wavelength when the grating element surface isformed.

According to this preferable example, unnecessary scattered lightgenerated by the grating element surface can be prevented from beingprojected on an image sensor and decreasing the image performance.

Also, in this case, it is preferable that the grating element surfacehas a kinoform profile.

Furthermore, in the optical system for reading in accordance with thepresent invention, it is preferable that the lens having the gratingelement surface is made of glass or of plastic. According to thispreferable example, a grating element surface having a kinoform profilewith excellent transcription performance can be achieved.

In an optical system for reading in accordance with the presentinvention, it is preferable that the lens having the grating elementsurface is formed from an infrared absorbing material. According to thispreferable example, particularly, unnecessary light in the infraredspectrum generated by the grating element surface can be prevented frombeing projected on an image sensor and decreasing the imagingperformance, so that good imaging performance can be ensured.

Furthermore, in the optical system for reading in accordance with thepresent invention, it is preferable to satisfy

0.2<y/Y<0.6  (13)

where Y is the maximum height of a manuscript and y is the maximumheight of an image sensor.

According to this preferable example, miniaturization of the opticalsystem for reading can be achieved.

Also, in this case, it is preferable that the meridional image surfacehas a better imaging performance than the sagittal image surface.According to this preferable example, precision of reading imageinformation or code information can be enhanced, so that erroneousrecognition can be prevented.

Furthermore, an imaging reading apparatus in accordance with the presentinvention comprises the optical system for reading in accordance withthe present invention, an image sensor for converting the imageinformation that is imaged by the optical system for reading intoelectric signals, and a circuit portion for processing the electricsignals to process the image information. According to the structure ofthis image reading apparatus, the size of the entire image readingapparatus can be smaller than that of a conventional one, and also animage reading apparatus with good imaging performance can also beachieved.

Furthermore, a bar code reader in accordance with the present inventioncomprises the optical system for reading in accordance with the presentinvention, an image sensor for converting the bar code information thatis imaged by the optical system for reading into electric signals, and asignal processing circuit having a circuit portion for decoding the barcode information. According to the structure of this bar code reader,the size of the entire bar code reader can be smaller than that of aconventional one, and a bar code reader with good imaging performancecan also be achieved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a device for calculating diffraction efficienciesaccording to a first embodiment of the present invention.

FIG. 2 is a block diagram of the device for calculating diffractionefficiencies according to the first embodiment of the present invention.

FIG. 3 illustrates an algorithm for the device for calculatingdiffraction efficiencies according to the first embodiment of thepresent invention.

FIG. 4 illustrates a data array for the device for calculatingdiffraction efficiencies according to the first embodiment of thepresent invention.

FIG. 5 illustrates a calculation algorithm for the device forcalculating diffraction efficiencies according to the first embodimentof the present invention.

FIG. 6 illustrates an algorithm for calculating diffraction efficienciesusing an FFT.

FIGS. 7a-b illustrates the light intensity distribution of asemiconductor laser.

FIG. 8 illustrates a calculation algorithm for the device forcalculating diffraction efficiencies according to a second embodiment ofthe present invention.

FIG. 9 illustrates an algorithm for the device for calculatingdiffraction efficiencies according to a third embodiment of the presentinvention.

FIGS. 10a-b illustrates the calculation of relief profiles afterprocessing in a third embodiment of the present invention.

FIG. 11 shows an example how relief profiles after processing arecalculated from a design relief profile with a device for calculatingdiffraction efficiencies according to a third embodiment of the presentinvention.

FIG. 12 illustrates an algorithm for calculating relief profiles afterprocessing, taking the feed speed of the processing bit intoconsideration.

FIGS. 13a-b illustrates a process for calculating relief profiles afterprocessing, taking the feed speed of the processing bit intoconsideration.

FIG. 14 illustrates a calculation algorithm for the device forcalculating diffraction efficiencies according to a fourth embodiment ofthe present invention.

FIG. 15 is a drawing showing the structure of a lens-shape measurementapparatus according to the fifth embodiment.

FIG. 16 illustrates an algorithm for the lens-shape measurementapparatus according to the fifth embodiment.

FIGS. 17a-b illustrates the data processing for eliminating amacroscopic curved surface shape from the measured shape data.

FIG. 18 illustrates an algorithm for lens design according to a sixthembodiment of the present invention, taking diffraction efficienciesinto consideration.

FIG. 19 is a schematic view of an objective lens for an opticalinformation recording/reproducing apparatus according to a ninthembodiment of the present invention and the light paths therein.

FIG. 20 is a structural drawing of an optical head according to a tenthembodiment of the present invention.

FIG. 21 illustrates an imaging lens according to an eleventh embodimentof the present invention.

FIG. 22 is a structural drawing of an image pickup device according to atwelfth embodiment of the present invention.

FIG. 23 is a cross sectional view showing the configuration of a lenswith a grating element of the thirteenth embodiment in accordance withthe present invention.

FIG. 24 is a graph showing the relationship between the ray height andthe phase delay of the lens with a grating element of the thirteenthembodiment in accordance with the present invention.

FIG. 25 is a graph showing the relationship between the ray height andthe phase delay of the lens with a grating element of the thirteenthembodiment in accordance with the present invention, and a schematicdiagram showing a specific relief profile of a diffraction elementformed from the graph.

FIG. 26 is a cross sectional view showing the configuration of a lenswith a grating element of the fourteenth embodiment in accordance withthe present invention.

FIG. 27 illustrates a graph showing the relationship between the rayheight and the phase delay of the lens with diffraction element of thefourteenth embodiment in accordance with the present invention, and aschematic diagram showing a specific relief profile of a diffractionelement formed from the graph.

FIG. 28 is a cross sectional view showing the configuration of a lenswith a grating element of the fifteenth embodiment in accordance withthe present invention.

FIG. 29 illustrates a graph showing the relationship between the rayheight and the phase delay of the lens with diffraction element of thefifteenth embodiment in accordance with the present invention, and aschematic diagram showing a specific relief profile of a diffractionelement formed from the graph.

FIG. 30 is a schematic diagram showing the ray paths of axial rays andabaxial rays in the lens with a grating element of the fifteenthembodiment in accordance with the present invention.

FIG. 31 is a schematic diagram showing the configuration of an imagingapparatus of the sixteenth embodiment in accordance with the presentinvention.

FIG. 32 is a schematic diagram showing the configuration of a readingapparatus of the seventeenth embodiment in accordance with the presentinvention.

FIG. 33 is a cross sectional view showing one example of an opticalsystem for reading of the eighteenth embodiment in accordance with thepresent invention.

FIGS. 34a-e shows drawings of various aberrations of the optical systemfor reading in FIG. 33.

FIG. 35 is a cross sectional view showing another example of the opticalsystem for reading of the eighteenth embodiment in accordance with thepresent invention.

FIGS. 36a-e shows drawings of various aberrations of the optical systemfor reading in FIG. 35.

FIG. 37 is a cross sectional view showing one example of an opticalsystem for reading of the nineteenth embodiment in accordance with thepresent invention.

FIGS. 38a-e shows drawings of various aberrations when the opticalsystem for reading in FIG. 37 is moved closest to the object side.

FIGS. 39a-e shows drawings of various aberrations when the opticalsystem for reading in FIG. 37 is moved closest to the image side.

FIG. 40 is a drawing for explaining the error analysis of Sweatt'smodel.

FIG. 41 is another drawing for explaining the error analysis of Sweatt'smodel.

FIG. 42 is an expanded sectional view of the image side surface of alens before it is converted to a grating element surface.

FIG. 43 is an expanded sectional view of a grating element surfaceformed by converting the lens surface shown in FIG. 42.

FIG. 44 is an expanded sectional view showing a kinoform profile of agrating element surface.

FIG. 45 is a schematic diagram showing an image reading apparatus of thetwelfth embodiment in accordance with the present invention.

FIG. 46 is a schematic diagram showing an image reading apparatus of thetwenty-first embodiment in accordance with the present invention.

FIG. 47 is a schematic diagram showing a bar code reader of thetwenty-second embodiment in accordance with the present invention.

FIG. 48 is a schematic diagram showing a bar code reader of thetwenty-third embodiment in accordance with the present invention.

FIGS. 49a-b is a schematic drawing illustrating how a die for thediffraction lens is cut with a diamond bit.

FIGS. 50a-e is a schematic drawing illustrating how a die for thediffraction lens is cut with a diamond bit, and a lens formed with sucha die.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention will be better understood from the following detaileddescription when considered with reference to the accompanying drawings.

First Invention

First Embodiment

When a diffraction lens is cut with a cutting bit, the extent ofdeformation due to the cutting bit changes from grating ring to gratingring. The deforming influence of the cutting bit on grating rings with alarge grating ring interval (pitch) is relatively small. On the otherhand, its influence on grating rings with a short grating intervalbecomes severe.

The grating ring pitch in a center portion of a diffraction lens isgenerally large, and becomes smaller towards a peripheral portion of thelens.

Therefore, the diffraction efficiency near the center of the lensdiffers from the diffraction efficiency near its periphery. Thediffraction efficiency of the entire lens can be found by determiningthe weighted average of the diffraction efficiencies of each lensportions.

EXAMPLE 1

FIG. 1 is a drawing of a computing device for calculating thediffraction efficiency in a first embodiment of the present invention.

Such a computing device according to this embodiment comprises a maincomputer 101, a display 102, a floppy-disk drive (FDD) 103, a keyboard104, a hard-disk drive (HDD) 105 and a printer 106. Each device isconnected to the main computer 101 with a connection cable 107. The maincomputer 101 incorporates a processing unit and a local memory device.

FIG. 2 illustrates the structure of such a computing device. Data isentered with the keyboard or read in with the FDD, and stored with theHDD. Data that is necessary for a computation is read from the HDD intothe local memory. The processing unit performs the necessarycomputations and the result is stored in the HDD. The results of thecomputations are output on the display or the printer.

A computer program for calculating the diffraction efficiency with acomputer is stored in the HDD. The processing unit loads the programfrom the HDD into the local memory, and performs the program. It is alsopossible to store the program on a floppy disk 108 or an optical disk109, as shown in FIG. 1.

“Memories” according to the present invention are means for storinginformation, and refer to information recording media such as floppydisks, hard disks, local memories, optical disks, print-outs from aprinter, etc. “Memory step” refers to the process of storing informationand applies to recording information on floppy disks, hard disks, localmemories, optical disks, etc. and printing information with a printer,etc.

Moreover, “processors” according to the present invention are means forperforming a numerical calculation with certain data, and generallyrefers to the processing unit of a computer. “Processing step” means theprocess of performing a numerical calculation with certain data.

“Repeating means” according to the present invention are means forrepeating the operation of a certain processing unit with a computerprogram. It is also possible that the operator of the computer sendsinstructions to repeat a calculating operation to the computer via aninput such as the keyboard. “Repeating step” means the repetition of acertain step (procedure).

“To retrieve information from a memory” means, for example, to read datafrom a floppy disk with the FDD, to read data from a hard disk with theHDD, to read data from an optical disk with an optical disk drive, toread data from the local memory, or to enter data that has been printedout by the operator of the computer via the keyboard.

A “recording medium on which a program is stored” according to thepresent invention is, for example, a floppy disk, a hard disk, anoptical disk, or a print-out from a printer, and refers to any mediumfor storing software for a computer.

It is possible that due to the advancement of computer technology newmeans (and steps) in accordance with the above explanations will bedeveloped in the future. However, it is to be understood that thepresent invention encompasses these newly developed devices and methods,if their function is similar to the function of the means (and steps) ofthe present invention. The present invention does not depend on aparticular device or method, but rather on the functions of these means(and steps). For example, it is possible that an information terminalconnected to a network via a network cable is used instead of therecording medium, such as the floppy disk, to send and receive data fromthis information terminal. However this would correspond to “retrieveinformation from a memory” in the present invention.

Furthermore, in the following, “devices” comprising certain “means” areexplained mainly to avoid duplicate explanations. However, theseexplanations also refer to “methods” comprising “steps”, or tocomputer-readable “recording media” storing a program for executing“steps” on a computer.

A device according to the present example calculates the weightedaverage of the diffraction efficiency of a diffraction element that isdivided into a plurality of regions, according to the formula$\begin{matrix}{E_{j} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mj}}}} & (1)\end{matrix}$

wherein η_(mj) is the diffraction efficiency of the j-th orderdiffraction light in the m-th region, and W_(m) is the weight for them-th region.

W_(m) must satisfy the equation $\begin{matrix}{{\sum\limits_{m = 1}^{M}W_{m}} = 1} & (15)\end{matrix}$

so that Equation (1) corresponds to the weighted average of η_(mj).

However, to facilitate the calculation, Equation (15) does notnecessarily have to be satisfied.

FIG. 3 shows an algorithm for calculating the above equation. In thepresent example, the diffraction lens is divided into M regions.

The diffraction efficiency data and the weights of these M regions havebeen stored beforehand into the memory.

FIG. 4 is an outline of the memory format for the diffraction efficiencydata stored in a first memory and the weight data stored in a secondmemory.

FIG. 4(a) shows the structure of the first memory storing thediffraction efficiency data for calculating the 0th-, -1st- and1st-order diffraction efficiencies. When the diffraction efficiencies ofthree orders are calculated, this is a two-dimensional data array withM×3 elements. The data array can be included in a device that can storethe data and read necessary data, for example in a memory, such as themain memory of a computer or a floppy disk.

FIG. 4(b) shows the structure of a second memory for similarly storinginformation about the weight of each region. In this case, there is adata row with M data fields. This second memory can also be realizedusing any memory device of the computer.

In this specification, “memory” means internal or external storageregions of the main computer for storing such data arrays, data rows, orsingle data elements, and can be any memory region in a computingdevice. Below, explanations as to what memory regions are used in eachmemory are omitted, and the memory is simply referred to as “memory”.

Concerning the data arrays, expressions without subscript refer to theentire array, and expressions with subscript refer only to a singleelement of the array. For example, in the example of FIG. 4, “η” refersto the memory region of (M×3) elements in the computing device, and η₁₀refers to a single element therein.

In FIG. 3, the diffraction order for the computation is set in step2101, which is the first step. In the following step 2102, E_(i) isinitialized to 0 and the counter m for counting the regions isinitialized to 1. In the following step 2103, the diffraction efficiencyη_(mi) of the i-th order diffraction light at the m-th region and theweight W_(m) for the m-th region are read out from the first and thesecond memory, and the product of η_(mi) and W_(m) is added to E_(i).The following step 2104 determines whether the region counter m is equalto M, to decide whether the calculation has been terminated for allregions. If m=M is not true, then there are regions left that have notbeen calculated, so m is increased by 1 in step 2105, and the procedurereturns to step 2103. If in step 2104 m=M is true, the procedureadvances to step 2106. The steps 2102 to 2105 correspond to the firstprocessor of the present invention. Step 2106 determines whether acalculation for another diffraction order has to be performed. If acalculation of the diffraction efficiency of another order is necessary,the procedure advances to step 2107, i is set to the next diffractionorder, and the procedure is repeated from step 2102. When no calculationfor another diffraction order is necessary, the calculation isterminated.

By using the device of this example, the diffraction efficiency of anentire lens having regions with differing diffraction efficiency can becalculated precisely and with high efficiency.

In this example, the calculation is made for a plurality of diffractionorders. However, a calculation for only a single diffraction order ispossible by omitting the steps 2101, 2106, and 2107 that are providedfor calculating a plurality of diffraction orders from the algorithmshown in FIG. 3.

EXAMPLE 2

In Example 1, the diffraction efficiency of each region has to bedetermined beforehand and stored in memory before the calculationbegins. However, often the diffraction efficiency is unknown. In thatcase, the form and the refractive index, etc. of the diffraction lensare measured, and using this data, the diffraction efficiency of eachregion is determined. On the basis of the diffraction efficiency of eachregion, the diffraction efficiency of the entire lens can be calculated.The calculation algorithm for this case is shown in FIG. 5.

It is assumed that relief cross-section data of the diffraction lens,the wavelength of the light-source, the refractive index of the lensmaterial at this wavelength, and the weights for the grating rings havebeen stored in a third, a fourth, a fifth, and a second memoryrespectively.

In step 301, the number of grating rings is determined on the basis ofthe relief data stored in the third memory and stored in a memory M. Thegrating ring counter m is initialized to 1.

In step 302, the relief data for the m-th grating ring is retrieved fromthe third memory, and the wavelength and the refractive index data areretrieved from the fourth and the fifth memory. The diffractionefficiency of the m-th grating ring is calculated and the result isstored in a region of memory η corresponding to the first memory. Thisstep 302 is the second processor of the present invention.

Step 303 determines whether step 302 has been performed for all gratingrings. If m=M is not true, then there are rings left for which thecalculation has not been performed, so m is increased by 1 in step 304,and the procedure returns to step 302. These steps 303 and 304correspond to a first repeating means. If in step 303 m=M is true, thismeans that step 302 has been performed for all grating rings, and thediffraction efficiencies of all rings are stored in a memory ηcorresponding to the first memory.

In step 305, the diffraction efficiency of the entire lens isdetermined. When all steps from step 301 to step 304 are performed, thediffraction efficiencies of all grating rings are stored in the memoryη, which corresponds to the first memory. The second memory stores theweights as already-known information. Consequently, by performing instep 305 the algorithm already explained for Example 1, the diffractionefficiency of the entire lens can be calculated.

Using the device according to this example, the lens diffractionefficiency of the entire lens can be calculated by evaluating its reliefprofile and refractive index, even when the diffraction efficiencies ofthe individual grating rings is not known, so that useful informationfor the design of optical systems can be obtained.

EXAMPLE 3

In Example 2, an example for an algorithm where one grating ring of thediffraction lens corresponds to one region has been explained. The pitchbetween the grating rings of the diffraction lens is large in a centerportion of the lens and becomes smaller towards the lens periphery. Atthe lens periphery, the pitch of neighboring grating rings is almost thesame. In such a case, it can be assumed that the diffraction efficiencyof these grating rings is also almost the same. Consequently, when aplurality of rings with presumably almost the same diffractionefficiency is treated as one region, the memory capacity that isnecessary for the memory η and the memory W can be decreased. Moreover,the computational amount is decreased, so that the calculation can besped up.

EXAMPLE 4

Several methods are known for calculating the diffraction efficiency onthe basis of the detailed relief profile of a diffraction element. Inthe case of diffraction lenses, scalar diffraction theory using aFourier transformation can yield sufficiently satisfactory precision. Adetailed calculation algorithm for this case is shown in FIG. 6.

In step 401, cross-sectional data of the grating ring relief to becalculated is loaded as working data into a data array D held on thecomputing device. If the number of elements in the data array is a powerof 2, then a Fast Fourier Transformation (FFT) can be used, and thecomputation process can be sped up. To be specific, a number in theorder of 4096 elements is advantageous.

In step 402, the wavelength λ and the refractive index N are retrievedfrom the memory corresponding to the third and the fourth memory, and onthe basis of these figures, the complex amplitude of the transmittedlight is determined and stored in a complex array P with the same numberof elements as the data array D, held in the computing device.

In the following step 403, an FFT is performed on the complex array P.The Fourier coefficients resulting from this process are stored in thecomplex array P.

In step 404, the complex conjugates of all elements of the complex arrayP are multiplied, which gives real numbers. Then, the elements arenormalized so that the sum of all elements of the complex array Pbecomes 1. Thus, the diffraction efficiency for each order is stored inthe complex array P.

In step 405, the diffraction efficiency of the necessary order is readout from the complex array P and stored in the memory η, whichcorresponds to the first memory.

Second Embodiment

In the above embodiment, it was assumed that suitable values for theweights of each region of the diffraction lens are stored beforehand ina memory. However, if these weights can be calculated on the basis ofthe intensity distribution of a light source and the grating ringdiameter of the diffraction lens, then the time and effort of enteringthese data can be saved.

The amount of the light incident on each region of the diffraction lensdivided by the amount of light incident on the entire lens can be usedfor the weights.

When it can be assumed that the light incident on the diffraction lenshas a uniform intensity distribution, the area of each region divided bythe effective diameter of the lens can be calculated and the resultingvalue can be used for the weights.

EXAMPLE 5

The following explains how the weights can be calculated when thesurface area of each region is stored in a memory (sixth memory).

In this example, the region of the diffraction lens through which thelight beam passes (effective region) is divided into M regions, andS_(m) is the area of the m-th region. First of all, the areas of allregions stored in the sixth memory are retrieved and added to calculatethe area S_(t) of the effective region using the formula $\begin{matrix}{S_{t} = {\sum\limits_{i = 1}^{M}{S_{i}.}}} & (16)\end{matrix}$

Then, $\begin{matrix}{W_{m} = \frac{S_{m}}{S_{t}}} & (17)\end{matrix}$

is calculated for all m from m=1 to m=M.

A third processor of the present invention calculates the weights forall grating rings with the above equations.

The obtained weights W_(m) for each grating ring are stored in a memorythat corresponds to the second memory for storing the weightinformation. The determined weights satisfy the equation $\begin{matrix}{{\sum\limits_{m = 1}^{M}W_{m}} = 1.} & (15)\end{matrix}$

Consequently, the sum of the products of these weights and thediffraction efficiencies of each region is a weighted average, whereinthe diffraction efficiency of each region is weighted with the area ofthat region.

EXAMPLE 6

If the diffraction lens consists of concentric grating rings, then theweights can be calculated on the basis of the radius of each gratingring instead of the area of each grating ring.

Here, the grating rings are counted from the center of the lens, and thetotal number of rings is M. That is to say, the grating ring in thecenter of the lens is the first ring, and the outermost ring is the M-thgrating ring. When the radius of the m-th grating ring is expressed byR_(m), then the radius R_(M) of the outermost grating ring is theeffective radius of the lens. When the radii R_(m) are stored in a dataarray corresponding to the seventh memory, the radii R_(m) are retrievedsequentially and the weights are calculated using $\begin{matrix}{W_{1} = {\frac{R_{1}^{2}}{R_{M}^{2}}\quad {and}}} & (3) \\{{W_{m} = {\frac{R_{m}^{2} - R_{m - 1}^{2}}{R_{M}^{2}}\quad \left( {m > 1} \right)}},\quad {wherein}} & (4)\end{matrix}$

R_(m): radius of the math grating ring counting from the center of thelens;

W_(m): weight of the m-th grating ring

M: number of grating rings

m: index of grating rings counted from the lens center

The results of these calculations are stored in the elements of theweight memory W, which corresponds to the second memory.

Thus, the weights W_(m) are proportional to the areas of the gratingrings. The determined weights satisfy the equation $\begin{matrix}{{\sum\limits_{m = 1}^{M}W_{m}} = 1.} & (15)\end{matrix}$

Consequently, the sum of the products of these weights and thediffraction efficiencies of each region is a weighted average, whereinthe diffraction efficiency of each region is weighted with the area ofthat region.

EXAMPLE 7

When a laser light source is used, the intensity distribution of theemitted light is not uniform, but is known to resemble a Gaussdistribution. In the case of a semiconductor laser, the emitted lightbeam is elliptic.

FIG. 7(a) is a schematic drawing of the light beam emitted from asemiconductor laser. A semiconductor laser light source 601 emits anelliptic light beam. The intensity distribution of the emitted beam inthe direction of the short axis (x-axis) 602 of the ellipse differs fromthe intensity distribution over the long axis (y-axis) 603 of theellipse. An example for the intensity distributions over these two axesis shown in FIG. 7(b). When such a light source is used, the result of acalculation where the weights are proportional to the area of thegrating rings deviates strongly from the actual value, which is highlyundesirable.

In this example, however, the light intensity in the center of the beam,as shown in FIG. 7(b), is normalized as 1, and the intensities(proportion relative to the peak values) over the x-axis and the y-axisin the effective radius 604 of the lens are I_(x) and I_(y) When theincident light intensity is as described in FIG. 7(b), more realisticweights that are proportional to the intensity of the light incident onthe grating rings, rather than proportional to the grating ring areas,can be calculated, if the data for I_(x) and I_(y) are available.

FIG. 8 illustrates a specific algorithm for such a calculation.

It is assumed that the incident light intensity data I_(x) and I_(y)have been stored beforehand in a memory that corresponds to an eighthmemory.

It is further assumed that the incident light has an intensitydistribution as shown in FIG. 7(b). In step 501, the entire light amountincident on the lens is calculated and the result of this calculationstored in another memory.

In step 502, the grating ring counter m is initialized to 1.

In step 503, the light amount incident on the m-th grating ring iscalculated using the grating ring radius information stored in theseventh memory as described in Example 6 and the information concerningthe intensity distribution of the light beam. In the following step 504,the light amount incident on the m-th grating ring as determined in step503 is divided by the total light amount as stored in memory. Thisquotient is stored as the weight W_(m) for the m-th grating ring in theweight memory W, which corresponds to the second memory. The steps 503and 504 correspond to the third processor of the present invention.

In step 505, it is verified whether the steps 503 and 504 have beenperformed for all grating rings. If m=M is not true, the procedureadvances to step 506, m is increased by 1, and the steps 503 and 504 arerepeated. If m=M is true, this means that the steps 503 and 504 havebeen performed for all grating rings. In this case, the weights of allgrating rings have been stored in the memory W.

In accordance with this algorithm, weights that are substantiallyproportional to the light intensity of the beam incident on each gratingring can be determined. Moreover, the determined weights satisfy theequation $\begin{matrix}{{\sum\limits_{m = 1}^{M}W_{m}} = 1.} & (15)\end{matrix}$

Consequently, the sum of the products of these weights and thediffraction efficiencies of each region is a weighted average, whereinthe diffraction efficiency of each region is weighted with the lightintensity that is incident in this region.

Consequently, in accordance with this example, the calculation of thediffraction efficiency with consideration of the light intensitydistribution of the light that is incident on the lens becomes possible.

Third Embodiment

In the above embodiments of a device for calculating diffractionefficiencies, it was assumed that the relief profile is already known.However, when, for example, the relief profile design data at the stageof the lens design, and the cutting bit data for processing the lens orthe feed speed of the cutting bit are known, the relief profile afterthe processing can be calculated on the basis of the relief profiledesign. In other words, on the basis of this information, thediffraction efficiency of the finally obtained lens can be calculatedtaking into account the change of the relief profile of the designedlens due to processing.

The following example is an example for forming a diffraction lens usinga diffraction lens mold that was cut with a cutting bit. However, thepresent invention is not limited to this, and can be equally appliedwhen no mold is used and the diffraction lens is directly cut with acutting bit.

EXAMPLE 8

FIG. 9 shows a computational algorithm performed by the device forcalculating diffraction efficiencies according to the third embodimentof the present invention.

First of all, the data necessary for the calculation is entered. Thismeans that the design shape of the diffraction lens relief, the endradius of the cutting bit for cutting the mold, the wavelength of thelight source used with the lens, and the refractive index of the lensmaterial are entered and stored in that order in memories thatcorrespond to the ninth, the tenth, the fourth, and the fifth memory.

In step 701, the number of grating rings of the diffraction lens isstored in the memory M, and the grating ring counter m is initialized to1.

In step 702, the relief profile after the processing is determined onthe basis of the relief profile design data, and stored in a reliefprofile memory, which corresponds to the third memory.

The relief profile design data of the m-th grating ring and the noseradius t of the end of the cutting bit are retrieved from the memoriescorresponding to the ninth and the tenth memory.

FIG. 10 illustrates the procedure performed during step 702. In FIG.10(a), numeral 801 is a saw-tooth-shaped relief design. When the lens ismanufactured using a mold by press-forming or injection molding, therelief profile after the processing has a rounded shape that is formedas the depressed vertex 802 of the mold (which becomes a protrudingvertex of the lens) and has the radius t of the cutting bit nose. Thatis to say, in the case of the relief 801, the vertex 802 can be roundedoff with the radius t. A circular arc 803 with the radius t is inscribedin the relief 801, so that the relief profile 804 shown in FIG. 10(b) isobtained after the processing. This relief profile 804 is stored in amemory for storing relief profiles, which corresponds to the thirdmemory of the present invention. When the lens is manufactured bycutting a lens material with a cutting bit, the depressed portions ofthe lens relief can be rounded off with the radius t. This step 702corresponds to the fourth processor of the present invention.

In step 703, the diffraction efficiency of the grating rings iscalculated. In this step, the relief profiles, the wavelengths, and therefractive indices are retrieved from the third, the fourth, and thefifth memory respectively, as explained for example in Example 2. Thediffraction efficiency is calculated, and the result of this calculationis stored in the memory η, which corresponds to the first memory.

Step 704 checks whether m=M is true. If m=M is not true, the procedureadvances to step 705, m is increased by 1, and steps 702 and 703 arerepeated. The steps 704 and 705 serve as both the first and the secondrepeating means. When in step 704 m=M is true, this means that steps 702and 703 have been performed for all grating rings, and the diffractionefficiencies of all rings are stored in memory η, which corresponds tothe first memory.

In step 706, the weight W is determined for each grating. The specificcalculations performed in this step have already been explained forExample 5, Example 6, and Example 7, so that a further explanation isomitted here. The weight information obtained in step 706 for eachgrating ring, is stored in the memory W, which corresponds to the secondmemory.

In step 707, the diffraction efficiency of the entire lens isdetermined. The specific calculations performed in this step are thesame as explained in Example 1, whereby a further explanation may beomitted.

By using the device of this embodiment, the diffraction efficiency canbe calculated on the basis of the lens design data and the processingdata of the cutting bit.

For comparison, FIG. 11 shows examples of relief profiles afterprocessing as calculated with a device according to this embodiment.

Numerals 2301 and 2306 indicate relief profile designs with 25 μm and127 μm pitch respectively, and 1.292 μm depth (note that the scaling invertical and horizontal direction in FIG. 11 is not equal). When therefractive index n of the lens material is 1.5262 and the wavelength λof the light-source is 680 nm, the depth D satisfies the equation$\begin{matrix}{D = {\frac{\lambda}{n - 1}.}} & (18)\end{matrix}$

Consequently, ignoring surface reflections, the designed reliefs 2301and 2306 in FIG. 11 have a diffraction efficiency of 100% forfirst-order diffraction light. When the mold for such a designed reliefis processed using a cutting bit with a nose radius of 10 μm, then thecalculated relief profiles are as indicated by the numerals 2302 and2307. Furthermore, when a cutting bit with a nose radius of 20 μm isused for the processing, then the calculated relief profiles are asindicated by the numerals 2304 and 2309. The chain double-dashed lines2303, 2305, 2308, and 2310 indicate the grating ring relief profiledesigns 2301 and 2306. Moreover, the diffraction efficiencies forfirst-order diffraction light were calculated for these grating ringsusing FFT. The result of this calculation was a diffraction efficiencyof 100% for the reliefs 2301 and 2306, 94.3% for relief 2302, 90.0% forrelief 2304, 73.5% for relief 2307, and 54.5% for relief 2309.

EXAMPLE 9

Depending on the feed speed of the processing bit, cutting traces mayremain on the relief after the processing. Because the waviness of therelief profile due to these cutting traces after the processing isperiodic, it causes diffraction light. As a result, the lens diffractionefficiencies of the orders that are actually utilized drop.Consequently, when a simulation is performed under consideration of thecutting traces, the relation between the feed speed of the processingbit and the resulting lens efficiency can be established. This data canbe useful for examining lens manufacturing processes.

This calculation can be performed when the algorithm in FIG. 12 is usedfor the fourth processor indicated as step 702 in the explanation ofExample 8. FIG. 13 explains this algorithm.

In FIG. 13(a), the solid line 901 indicates a saw-tooth-shaped reliefdesign. The nose radius of the processing bite is t, and the feed amountof the processing bit per revolution of the mold during the machining iss. It is assumed that this information has been stored beforehand in aninth, a tenth, and an eleventh memory of the computing device,respectively.

In step 1001 in FIG. 12, the relief profile design is retrieved from thememory corresponding to the ninth memory and stored temporarily asworking data in a data array held in a memory of the computer.

Then, in step 1002, using the value held in the memory s, whichcorresponds to the eleventh memory, the point where the relief contactsthe tip of the cutting bit is determined, and stored temporarily asworking data in a data array P held in a memory of the computer. To bespecific, parallel lines 902 are drawn in intervals in relief pitchdirection (i.e. sideways in FIG. 13) that are equal to the feed speed s.The points of intersection P₁, P₂, P₃, . . . , P_(G−1), P_(G), betweenthese lines 902 and the designed relief 901 are determined and theircoordinates are stored in memory. Here, it is assumed that the totalnumber of points of intersections is G.

In the following step 1003, the counter g is initialized to 1.

In step 1004, the circular arc C_(g) with the radius t that contacts thedesigned relief tangentially in P_(g) is determined.

In step 1005, it is verified whether the circular arc determined in step1004 intersects with the designed relief profile. If the circular arcintersects with the designed relief profile (for example, in the case ofcircular arc C_(G) in FIG. 13), the procedure advances to step 1007. Ifit does not intersect the designed relief profile, the procedureadvances to step 1006.

In step 1006, the shape of the circular arcs determined above is storedin an array for storing shapes, and the procedure advances to step 1007.

In step 1007, it is verified whether step 1004 has been performed for 20all points of intersection P. If g=G is not true, the procedure advancesto step 1008, g is augmented by 1, and the next calculation isperformed. If g=G is true, this means that the calculation is finished.

Thus, data 903 of the shape after the processing, under consideration ofthe cutting feed speed, as illustrated in FIG. 13(b), is stored in anarray for storing shapes. This data is stored in a memory thatcorresponds to the third memory.

Fourth Embodiment

When the lens is used over a broad wavelength range, as in cameralenses, the diffraction efficiency has to be calculated for a pluralityof wavelengths. In this case, the calculations described in the aboveexamples can be repeated for the necessary wavelengths components, butthis will increase the computational amount proportionally to thecalculated number of wavelengths.

Here, the relief profile after processing is determined from thedesigned relief profile, for example as illustrated for Example 8, usingthe method of finding the tangential circular arcs at the designedrelief, and determining the envelope of these circular arcs. Therefore,the computational amount is large. Since the calculation for determiningthe relief profile after processing is the same for the calculation ofthe diffraction efficiency at every wavelength, the relief profile canbe calculated once and then stored. The result of this calculation canbe used for the diffraction efficiency calculation of every wavelength,so that the computational amount is lower than if the calculationsexplained in the previous examples are simply repeated for allwavelengths. Thus, compared to this case, the procedure is sped up. Thesame holds true for the calculation of the weights.

Moreover, when the relief profile after processing of a certain gratingring has been determined from the designed relief profile, it ispossible to calculate the diffraction efficiencies at all wavelengthsusing the relief profile after processing, store only the calculateddiffraction efficiencies in the memory, and then, calculate the reliefprofile after processing of the next grating ring. If the calculation isperformed in this order, the necessary memory capacity and the time forretrieving information can be decreased compared to performing thecalculation in the order (a) first, calculating the relief profile afterprocessing for all grating rings, (b) store those relief profiles in amemory, (c) load the stored relief profiles after processing one afteranother and calculate the diffraction efficiencies of all relevantwavelengths one after another, because the data volume of the reliefprofiles after processing is large.

EXAMPLE 10

FIG. 14 is a diagram that explains an algorithm for a device forcalculating diffraction efficiencies according to the fourth embodimentof the present invention.

It is assumed that the relief profile design, the processing bit data, aplurality of wavelengths, refractive indices for this plurality ofwavelengths, and the radii of the grating rings of the diffraction lenshave already been stored in memories that correspond to the ninth, thetenth, the fourth, the fifth, and the seventh memory, respectively.

In step 1101, an initialization is performed to prepare the start of thecalculation. The memories corresponding to the first, the second and thethird memory are held in the computing device, the number of lensgrating rings is initialized to M, the number of wavelengths to becalculated is initialized to L, and the memory m is initialized to 1.

In step 1102, the relief profile design data and the nose radius of thecutting bit are retrieved from the memories corresponding to the ninthand the tenth memory. Then, the relief profile of the ring afterprocessing is calculated and stored in the memory corresponding to thethird memory. The precise calculations of this step correspond to thoseof step 702 in Example 8. Step 1102 corresponds to the fourth processorof the present invention.

In step 1103, the wavelength counter is initialized to 1. In thefollowing step 1104, the relief profile after processing, an l-thwavelength, and the material's refractive index data at the l-thwavelength are retrieved from the memories corresponding to the third,the fourth and the fifth memory. Then, the diffraction efficiency iscalculated and stored in the memory corresponding to the first memory.Step 1104 corresponds to the second processor.

Step 105 determines whether l=L is true. If l=L is true, this means thatstep 1104 has been performed for all wavelengths, and the procedureadvances to step 1107. If l=L is not true, this means that there arestill wavelengths for which the calculation has not been performed, andthe procedure advances to step 1106, where l is increased by 1, and step1104 is repeated. Step 1105 and step 1106 correspond to the thirdrepeating means.

Step 1107 determines whether m=M is true. If m=M is true, this meansthat steps 1102, 1103, and 1104 have been performed for all gratingrings, so that the procedure advances to step 1109. If m=M is not true,this means that there are still grating rings for which the calculationhas not been performed, and the procedure advances to step 1108, where mis increased by 1, and steps 1102, 1103, and 1104 are repeated. Step1107 and step 1108 correspond to the fourth repeating means.

In step 1109, information about the grating ring radii is retrieved fromthe memory corresponding to the seventh memory. Then, the weights arecalculated and stored in the memory corresponding to the second memoryfor storing weights. The calculation in this step is the same as thecalculation explained in Example 6, so a further explanation is omittedhere. The information about the weights, which is stored in the secondmemory, cannot only be obtained by calculation from the grating ringradii as explained in Example 6, but also by the calculations explainedin Example 5 or Example 7 of the second embodiment.

In step 1110, the wavelength counter l is initialized to 1. Then, instep 1111, the diffraction efficiencies and the weights of all gratingrings corresponding to the l-th wavelength is retrieved from the firstand the second memory, and the refractive index of the entire lens atthe l-th wavelength is calculated. Step 1112 determines whether l=L istrue. If l=L is true, this means that step 1111 has been performed forall wavelengths, and the calculation is concluded. If l=L is not true,this means that there are still wavelengths for which the calculationhas not been performed, and the procedure advances to step 1113, where lis increased by 1, and step 1111 is repeated. In accordance with steps1110, 1111, 1112, and 1113, $\begin{matrix}{E_{jl} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mjl}}}} & (5)\end{matrix}$

is calculated wherein

j: integer indicating the order of diffraction light

l: index of the wavelengths number

E_(jl): diffraction efficiency for j-th order diffraction light of thediffraction lens at the l-th wavelength

M: positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated

m: index of the region number

W_(m): weight for the m-th region

η_(mjl): diffraction efficiency for the j-th order diffraction light ofthe m-th region at the l-th wavelength

These steps 1110, 1111, 1112, and 1113 correspond to the firstprocessor.

Using the calculation algorithm of this example, a calculation for manywavelengths can be performed with comparatively small memory capacityand high speed. Consequently, the calculation time for designing a lensfor use over a broad wavelength spectrum, such as a camera lens, can beshortened, which can be a great advantage.

Fifth Embodiment

The shape of the manufactured diffraction lens and the lens-molding diecan be measured using a high-precision shape-evaluation device such as asurface-roughness meter. To know to what extent the precision of thelens shape and the lens-molding die shape influences the diffractionefficiency can be very important in terms of quality management, such asdetermination of tolerances or discrimination of defective products.

EXAMPLE 11

FIG. 15 is a drawing showing the structure of a lens-shape measurementapparatus according to the fifth embodiment.

A lens 1201 is placed on a stage 1202 for examination. The stage 1202 istranslated in horizontal direction by a stage control apparatus 1203. Anexamining needle 1204 is moved in vertical direction, controlled by anexamining-needle control apparatus, so that it touches the lens 1201.

The stage control apparatus 1203 and the examining-needle controlapparatus 1205 send the stage coordinates Y and the examining needlecoordinates Z to a processing unit 1206. Thus, a data array consistingof pairs of stage coordinates Y and examining needle coordinates Zserves as the lens shape data. A program for calculating diffractionefficiencies with a computer is stored on the hard disk drive (HDD)1207. The processing unit 1206 loads this program to control theapparatuses and determine the data. The data that is necessary tocalculate the diffraction efficiency is entered over a keyboard 1208. Adisplay 1209 displays the calculation result and the measured data.

FIG. 16 is a software algorithm for calculating diffraction efficiencieswith a computer in accordance with this example.

Step 1301 is the step for data input. In particular, data specifying themeasurement, such as the measurement range on the lens to be examinedand the number of sampling points, and data necessary for calculatingthe diffraction efficiency such as the refractive index of the glassmaterial and the wavelengths are entered in this step.

In step 1302, the lens shape is measured. The stage coordinates whenmoving the stage 1202 with the stage control apparatus 1203 inhorizontal direction and the coordinates of the examining needleobtained from the examining needle control apparatus 1205 are stored ina measurement data array U that has been previously reserved in a memoryregion of the computer.

The solid line in FIG. 17(a) is an example of the data for a combinedrefraction/diffraction lens measured with a surface roughness meter. Thevertical axis 2202 corresponds to the optical axis of the measured lens.Thus, the vertical direction corresponds to the sag of the lens. Thehorizontal axis 2203 corresponds to the direction from the lens centerto the periphery (radial direction).

The following step 1303 determines whether the measured data belongs toa die or to a lens. If the measured data belongs to a lens, then theprocedure advances to step 1305. If the measured data belongs to a die,the procedure advances to step 1304, where the data is reversed toproduce lens shape data, which is stored in the measurement data arrayU.

Step 1305 fits the measured data, for example by the least-squaresmethod, to an aspherical surface, a spherical surface or a plane. Thefollowing step 1306 eliminates the shape of the aspherical surface,spherical surface or plane determined in step 1305 from the measurementdata array U, and stores the resulting data in a relief profile array L.

FIG. 17 explains the procedure for steps 1305 and 1306. To calculate thediffraction efficiency, a microscopic undulation of the lens surface isimportant. However, when the diffraction lens is measured with ashape-measurement device, such as a surface roughness meter, thismicroscopic undulation is superimposed on a macroscopic curved surface,as shown by the solid line 2201. Therefore, a procedure is necessary toremove this macroscopic curved surface portion from the measured data ofthe lens. The broken line 2204 in FIG. 17(a) is a plot of the asphericalpolynomial determined in step 1305. The relief profile 2205 in Figure(b)is the result of the subtraction of the macroscopic portion 2204 fromthe measured data 2201. This relief profile 2205 is stored in a shapearray L.

In step 1307, the grating ring counter m is initialized to 1. Step 1308calculates the diffraction efficiency of the m-th grating ring, which isstored in the memory corresponding to the first memory. Step 1309verifies whether this calculation has been performed for all gratingrings. If there are grating rings left for which the calculation has notbeen performed, then m is increase by 1 in step 1310, and step 1308 isrepeated. If step 1309 confirms that the calculation has been concludedfor all grating rings, the procedure advances to step 1311, where theweights for all grating rings are calculated and stored in the memorycorresponding to the second memory. In step 1312, the diffractionefficiency and the weight of each grating ring is retrieved from thefirst and the second memory respectively, and the diffraction efficiencyof the entire lens is determined. The calculation of the diffractionefficiency of the entire lens in steps 1307-1312 can be performed usingthe device for calculating diffraction efficiencies according to thefirst or the second embodiment of the present invention.

The present embodiment uses a shape measurement device with an examiningneedle. However, the same effect can be attained using an opticalnon-contact-type shape measuring device, a shape measuring deviceutilizing inter-atomic forces, etc.

Using the shape measurement device described in this embodiment, thediffraction efficiency can easily be calculated from the measured shapeof a diffraction lens or die for diffraction lenses.

Sixth Embodiment

FIG. 18 illustrates an algorithm for a lens design device according to asixth embodiment of the present invention, which takes the diffractionefficiency into consideration.

First of all, a target specification is selected (step 1401), then theinitial parameters of the lens are entered (step 1402). Next, theoptical properties at these parameters are calculated by ray-tracing(step 1403).

Then, it is verified whether these optical properties satisfy the targetspecifications (step 1404). If the lens properties satisfy the targetspecifications, the procedure advances to step 1406, and if they do notsatisfy the target specifications, the lens parameters are corrected atstep 1405, and the evaluation of the optical properties in step 1403 isrepeated.

In step 1406, a diffraction efficiency with consideration of processingis calculated. This calculation can be performed using the device forcalculating diffraction efficiencies explained in the third embodimentof the present invention.

Step 1407 determines whether the diffraction efficiency obtained in thecalculation satisfies the system design conditions. If the diffractionefficiency satisfies the system design conditions, the design isconcluded (step 1408), and if it does not satisfy the system designconditions, the lens parameters are corrected (step 1405), and theprocedure returns to step 1403, where the optical properties arecalculated.

To correct the lens parameters in order to improve the diffractionefficiency, the lens data can be amended such that the pitch of thediffraction lens becomes wider. Especially, widening the small pitchesnear the lens periphery has the effect of improving the diffractionefficiency. It is necessary to correct the aberration that arisesthrough the correction of the lens pitch by correcting the asphericalcoefficients of the lens.

Even when the power of the entire diffraction lens is reduced, thediffraction lens pitch can be widened up, which has the effect ofimproving the diffraction efficiency. In this case, if the diffractionlens is used for example for correction of chromatic aberration, thecorrection of the chromatic aberration is reduced. However, using thedesign method of the present embodiment, a lens can be designed withconsideration to the restrictions due to both correction of chromaticaberration and diffraction efficiency tolerance.

Moreover, when the method of calculating diffraction efficienciesaccording to the present invention is incorporated in lens designsoftware, the previous processes can be further simplified and an evenbetter design solution can be attained. To be even more specific, thediffraction efficiency under consideration of the processing can be usedfor one merit function (evaluation function) for the lens design. Thiscan easily be realized by incorporating a program for calculatingdiffraction efficiencies according to the present invention in lensdesign software. By doing so, the designer can specify the diffractionefficiency, similar to the aberration conditions, for the evaluationfunction, and a design solution that minimizes the evaluation functioncan be found using such widely-known optimization techniques as the DLSmethod.

This embodiment is useful for designing an optical system with harshrestrictions concerning the diffraction efficiency, if the diffractionefficiency under consideration of processing is known at the time oflens design.

Seventh Embodiment

The following is an explanation how a lens is designed with a lensdesign apparatus of the sixth embodiment of the present invention.

The present embodiment explains an example of the design of anachromatic lens for the correction of the chromatic aberration of arefraction lens with a diffraction lens. To correct the lens design dataat the design stage in order to improve the diffraction efficiency, thepitch of the diffraction lens is widened up. There are two approaches tothe pitch correction.

The first approach is to prolong the focal length of the diffractionlens. By doing so, the pitch can be widened up entirely, which improvesthe diffraction efficiency. When the focal length of the diffractionlens is prolonged under the restriction that the total focal length ofthe entire lens has to be constant, the focal length of the refractivelens has to be shortened to compensate this. Thus, the correctionconditions for the chromatic aberration cannot be satisfied, and theresult is a lens where the chromatic aberration is undercorrected.

The other approach is to widen the pitch at a peripheral portion of thelens. This is very effective to suppress a drop of the diffractionefficiency, which is considerable at a peripheral portion where thepitch is narrow. In this case, the chromatic aberration of a light beamthat is transmitted near the center of the lens is corrected, but thechromatic aberration for light beams that pass a peripheral portion ofthe lens becomes undercorrected.

Furthermore, lenses can be designed with a combination of the above twoapproaches. This means, the focal length of the diffraction lens isdesigned a little bit longer than according to the achromatismcondition, and the pitch at the lens periphery is widened up a littlecompared to the regular pitch. If the lens is designed like this, thenthe entire undercorrection of the chromatic aberration and theundercorrection of the chromatic aberration for the beams that pass thelens periphery are smaller than if the diffraction efficiency isimproved with only one of the two above approaches. As a result, thedeterioration of the optical characteristics can be reduced.

Thus, in a lens with corrected chromatic aberration that is designedusing the lens design apparatus of the sixth embodiment, the chromaticaberration tends to be undercorrected, but a lens can be obtained wherethe deterioration of the diffraction efficiency due to the manufacturingprocess where it is cut with a diamond bit can be reduced.

Eighth Embodiment

The following is an explanation of a combined refraction/diffractionlens according to an eighth embodiment of the present invention. Acombined refraction/diffraction lens is a lens where a diffraction lensconsisting of a plurality of concentric rings is arranged on the surfaceof at least one refraction lens.

The central wavelength for the lens design is λ₁ and the following andthe preceding wavelengths are λ₂ and λ₃. The refractive indices of thelens material at these wavelengths are n₁, n₂, and n₃. The partialdispersion coefficient ν_(g) of the refraction lens in the appliedwavelength region and the partial dispersion coefficient ν_(d) of thediffraction lens in the applied wavelength region are defined as$\begin{matrix}{{v_{g} = \frac{n_{1} - 1}{n_{2} - n_{3}}},{and}} & (19) \\{v_{d} = {\frac{\lambda_{1}}{\lambda_{2} - \lambda_{3}}.}} & (20)\end{matrix}$

Moreover, f_(g) is the focal length of the refraction lens, f_(d) is thefocal length of the diffraction lens, and the total focal length is f,and the focal lengths are selected so that $\begin{matrix}{{{\frac{1}{f_{g}\upsilon_{g}} + \frac{1}{f_{d}\upsilon_{d}}} = 0},} & (21)\end{matrix}$

then the chromatic aberrations at the wavelengths λ₁, λ₂, and λ₃ arecancelled.

In the design of regular optical systems, there is usually sometolerance for chromatic aberration, and it is mostly sufficient toreduce the chromatic aberration per glass lens or plastic lens by aboutone half. In that case, Equation (21) can be replaced with$\begin{matrix}{{{\frac{1}{f_{g}\upsilon_{g}} + \frac{1}{f_{d}\upsilon_{g}}} = {k\quad \frac{1}{f\quad v_{g}}}},} & (22)\end{matrix}$

In Equation (22), k is a factor that shows to what extent the chromaticaberration in a single glass (or plastic) lens is canceled. If k=0, thenthe chromatic aberration is zero, and if k=1, this means that nodiffraction lens is used.

Here, 0.1≦k≦0.9 is a preferable condition for correcting the chromaticaberration while maintaining a favorable diffraction efficiency. If k islower than that range, it is necessary to use a sharp cutting bit toobtain a satisfactory diffraction efficiency, so that the productivityworsens, since the number of grating rings on the lens is large and thegrating ring pitch becomes narrow. Moreover, when k is above this range,the correction of the chromatic aberration is not adequate, and theeffect of incorporating a diffraction lens becomes insufficient.

More preferable is that k is in the range 0.2≦k≦0.8.

Ninth Embodiment

FIG. 19 illustrates the outline of an objective lens according to theninth embodiment of the present invention and an optical path when usingit in an optical information recording and reproducing device.

An objective lens 1501 comprises a diffraction lens 1502 on an ingoingsurface of a refraction lens. The objective lens is thus a combinedrefraction/diffraction lens for use in an optical information recordingand reproducing device. Numeral 1503 indicates a protective plastic filmon an information recording medium, and numeral 1504 indicates aningoing light beam.

In the optical information recording and reproducing device, the emittedwavelength of the light source laser changes when the output powerchanges, so that it is preferable that the change of the focal length ofthe objective lens per change of wavelength is small. In the lensaccording to this embodiment, the refraction lens and the diffractionlens both have a positive refractive power, so that the chromaticaberration of the refraction lens is corrected by the diffraction lens.

The wavelength variation in a semiconductor laser as a light source foran optical information recording and reproducing device is about severalnm, so that an achromatism in the range of design wavelength ±10 nmshould be considered. This means, the partial dispersion should becalculated as λ₂=λ₁−10 nm, and λ₃=λ₁+10 nm.

When the numerical aperture (NA) of the lens is N, the minimum pitch pof the lens can be calculated approximately according to $\begin{matrix}{p = {\frac{\lambda_{1}\left( {v_{d} - v_{g}} \right)}{{Nkv}_{d}}.}} & (23)\end{matrix}$

In this equation, the light-source wavelength λ is approximately 650nm-800 nm, and NA is approximately 0.45-0.65.

Moreover, when a regular die for molding lenses is processed with acutting bit, it is preferable that the nose radius of the cutting bittip is about 10 μm, which yields a good productivity. When the cuttingbit tip is smaller than that, the diffraction efficiency can beimproved, but the productivity becomes worse, so a smaller tip is notpreferable.

In an objective lens for an optical information recording andreproducing device, 0.2≦k≦0.6 is a preferable range for theabove-mentioned factor k. If k is lower than this range, theabove-mentioned minimum pitch p for processing a lens or a die formolding lenses using a cutting bit with a nose radius of 10 μm becomesshort, which brings about deterioration of the diffraction efficiency.If k exceeds the above range, the effect of correcting chromaticaberration becomes insignificant, and there is no merit in incorporatinga diffraction lens.

Moreover, 0.3≦k≦0.55 is the condition for maintaining a satisfyingdiffraction efficiency when the numerical aperture of the lens is large,i.e. higher than 0.5. Because the minimum pitch becomes narrower whenthe numerical aperture is large, the lower limit of k has to be raised.Furthermore, the focus depth for a lens with high numerical aperture issmall, so that the upper limit has to be lowered to about 0.55.

EXAMPLE 12

The following is an example for the design of a lens for an opticalhead, which is a system combining a refraction lens and diffraction lens(combined refraction/diffraction lens), where the focal length of theentire optical system is 3 mm.

Table 1 shows the refractive indices of the lens material used for thedesign at several wavelengths.

TABLE 1 Wavelength (nm) Refractive Index λ₁   680 1.526231 λ₂   6701.526554 λ₃   690 1.525920 Under these conditions, ν_(g) and ν_(d) areν_(g) = 830.01735 and ν_(d) = −34.

The design results for a total focal length of f=3.0 mm and threedifferent factors k are shown in the Tables 2 to 4. These tables showthe result of the diffraction efficiency calculations performed with thedevice for calculating diffraction efficiencies according to the presentinvention when the diffraction lens was processed using a cutting bitwith 10 μm nose radius.

TABLE 2 k 0 f 3.0 f_(g) 3.122889 f_(d) 76.236825 Number of Grating Rings27 Minimum Pitch 31.3 μm Diffraction Efficiency 84.8%

TABLE 3 k 0.3 f 3.0 f_(g) 3.084978 f_(d) 108.90975 Number of GratingRings 19 Minimum Pitch 44.9 μm Diffraction Efficiency 89.3%

TABLE 4 k 0.55 f 3.0 f_(g) 3.0540816 f_(d) 169.41517 Number of GratingRings 12 Minimum Pitch 69.8 μm Diffraction Efficiency 92.3%

It follows from these tables, that the diffraction efficiency can beimproved when 0.3≦k.

The same calculation for a total focal length of 5 mm is illustrated inthe Tables 5 to 7.

TABLE 5 k 0 f 5.0 f_(g) 5.204815 f_(d) 127.06138 Number of Grating Rings44 Minimum Pitch 31.5 μm Diffraction Efficiency 85.0%

TABLE 6 k 0.3 f 5.0 f_(g) 5.14163 f_(d) 181.51625 Number of GratingRings 31 Minimum Pitch 45.0 μm Diffraction Efficiency 89.3%

TABLE 7 k 0.55 f 5.0 f_(g) 5.09136 f_(d) 282.35861 Number of GratingRings 20 Minimum Pitch 70.2 μm Diffraction Efficiency 93.1%

In the following, a lens with a focal length of 3 mm but designed from adifferent material is examined.

The refractive indices of the lens material at several wavelengths areshown in Table 8.

TABLE 8 Wavelength (nm) Refractive Index λ₁   680 1.511272 λ₂   6701.511567 λ₃   690 1.510987 Under these conditions, ν_(g) and ν_(d) areν_(g) = 881.50345, and ν_(d) = −34.0.

Under these conditions, ν_(g) and ν_(d) are ν_(g)=881.50345, andν_(d)=-34.0.

The calculation results are shown in Tables 9-11:

TABLE 9 k 0 f 3.0 f_(g) 3.1157114 f_(d) 80.779716 Number of GratingRings 25 Minimum Pitch 33.5 μm Diffraction Efficiency 85.6%

TABLE 10 k 0.3 f 3.0 f_(g) 3.08007158 f_(d) 115.39959 Number of GratingRings 18 Minimum Pitch 47.6 μm Diffraction Efficiency 89.7%

TABLE 11 k 0.55 f 3.0 f_(g) 3.0509885 f_(d) 179.51048 Number of GratingRings 12 Minimum Pitch 74.0 μm Diffraction Efficiency 93.2%

According to the above design examples, the diffraction efficiency canbe improved by setting k to a certain range, regardless of the lensmaterial or focal length.

In these examples, the grating ring radius r_(m) of the m-th gratingring was calculated in accordance with

 r_(m)={square root over (2mλ₁f_(d))}.  (24)

As a method for calculating the radius of the grating rings, methodssuch as using the high imaginary refractive index and other methods arewell known. By selecting the focal lengths of the refraction lens andthe diffraction lens such that k is within a certain range, arefraction/diffraction achromatic lens with excellent processability andno diminished diffraction efficiency can be designed. This main point ofthe present invention has of course the same effect when the gratingring radii are designed by another method.

Moreover, in this example, a lens for an optical head has beenexplained, but in an optical system with a light source that has thesame level of wavelengths variations as a semiconductor laser, a lenswith both high diffraction efficiency and good chromatic aberrationcorrection can be designed in accordance with the present invention.

Furthermore, in this example, the diffraction lens was arranged on theingoing plane of a refraction lens, but the same effect can of coursealso be attained if a diffraction lens is arranged on the outgoing planeof a lens.

Tenth Embodiment

The following is an explanation of an optical head according to a tenthembodiment of the present invention, with reference to accompanyingdrawings.

FIG. 20 is a structural drawing of an optical head according to thisembodiment.

A divergent light beam 1602 emitted from a semiconductor laser lightsource 1601 is collimated into a substantially parallel light beam 1604by a collimator lens 1603. The light beam 1604 passes a beam splitter1605 and an objective lens 1606 for an optical information recording andreproducing device according to the present invention focuses the lightbeam on a disk 1607. The light that is reflected from the disk 1607 iscollimated into a substantially parallel light beam by the objectivelens 1606, reflected by the beam splitter 1605, and focused on aphotodetector 1609 by an optical detection system 1608.

Because the output of the semiconductor laser light source 1601 duringrecording differs from the output during reproducing, the wavelengthalso differs a little. An objective lens according to the ninthembodiment is used for the objective lens 1606, so that the change ofthe focal length of the objective lens due to chromatic aberration issmall. Moreover, because the diffraction lens has a favorablediffraction efficiency, stray light can be reduced, so that a favorablesignal output can be obtained.

Eleventh Embodiment

The following is an explanation of an imaging lens according to aneleventh embodiment of the present invention, with reference to the 10accompanying drawings.

FIG. 21 is a structural drawing of an imaging lens according to thepresent invention. An imaging lens 1701 according to the presentinvention is a combined refraction/diffraction lens comprising adiffraction lens 1702 of a plurality of concentric grating ringsarranged on an ingoing surface of a refraction lens. The lens images aningoing light beam 1703 on an image plane 1704.

In this lens, the refraction lens and the diffraction lens both have apositive refracting power, and the chromatic aberration of therefraction lens is corrected by the diffraction lens.

The wavelength used in the case of an imaging lens is broad, and it isnecessary to consider not only the diffraction efficiency at theprincipal wavelength λ₁, but also the diffraction efficiencies at thewavelengths λ₂ and λ₃. When the diffraction efficiency deterioratesoutside the principal wavelength, the image obtained with that lenstends to flare, which is not desirable.

It is preferable that that factor k of the imaging lens of the presentinvention satisfies the equation

0.3≦k.

When k is lower than 0.3, then processing with an extremely sharpcutting bit is necessary to obtain a satisfactory diffractionefficiency, which lowers the productivity for manufacturing the lens.

It is even more preferable that the factor k satisfies the equation

0.4≦k≦0.7. The lower restriction of this equation is the condition underwhich a satisfactory diffraction efficiency can be attained in a brightlens with an f number of about 1.5. The upper restriction is thecondition for reducing the remaining chromatic aberration to one half ofthe chromatic aberration of a single refraction lens.

EXAMPLE 13

The following is a comparative discussion of three design examples for alens with a total focal length of the diffraction lens and therefraction lens of 5 mm, an f number of 1.55 and three different valuesof k.

For λ₁, λ₂, and λ₃, the visible wavelength region has been considered,and the D line (587.6 nm), the F line (486.1 nm) and the C line (656.3nm) have been chosen.

Table 12 shows these standard wavelengths for the design and therefractive index of the lens material at these wavelengths.

TABLE 12 Wavelength (nm) Refractive Index λ₁   587.6 1.524039 λ₂   486.11.530271 λ₃   656.3 1.520983 v_(g) 56.439526  v_(d) −3.452409 

Tables 13, 14, and 15 show the design for k=0, 0.4, and 0.7. In thesetables, the diffraction efficiencies have been calculated for processingwith a cutting bit with 10 μm nose radius using a device for calculatingdiffraction efficiencies of the present invention.

TABLE 13 Design Parameters k 0 f_(g) 5.3131153 f_(d) 84.842801 Number ofGrating Rings 27 Minimum Pitch 30.9 μm Diffraction Efficiency WavelengthDiffraction Efficiency λ₁ 85.5 λ₂ 76.9 λ₃ 80.9

TABLE 14 Design Parameters k 0.4 f_(g) 5.1791273 f_(d) 144.56557 Numberof Grating Rings 16 Minimum Pitch 52.7 μm Diffraction EfficiencyWavelength Diffraction Efficiency λ₁ 91.3 λ₂ 80.2 λ₃ 87.0

TABLE 15 Design Parameters k 0.7 f_(g) 5.0879875 f_(d) 289.13114 Numberof Grating Rings 8 Minimum Pitch 105.3 μm Diffraction EfficiencyWavelength Diffraction Efficiency λ₁ 92.1 λ₂ 80.6 λ₃ 87.8

If k=0, the number of grating rings is large, and the minimum pitch issmall. As a result, a satisfactory diffraction efficiency cannot beattained, even when the lens is processed using a cutting bit with anose radius of 10 μm.

On the other hand, if k=0.4 is chosen for the design, a favorablediffraction efficiency and a good productivity can be attained when acutting bit with a nose radius of 10 μm is used. If k=0.7 is chosen,even better results can be obtained.

In this embodiment, the grating ring radius r_(m) of the m-th gratinglens on the diffraction lens can be calculated according to

 r_(m)={square root over (2mλ₁f_(d))}.  (24)

As a method for calculating the radius of the grating rings, methodssuch as using the high imaginary refractive index and other methods arewell known. By selecting the focal lengths of the refraction lens andthe diffraction lens such that k is within a certain range, arefraction/diffraction achromatic lens with excellent processability andno diminished diffraction efficiency can be designed. This main point ofthe present invention has of course the same effect when the gratingring radii are designed by another method.

In this embodiment the D line, the F line, and the C line have beenchosen for λ₁, λ₂, and λ₃, but other conditions are possible,considering for example the spectral distribution of the object to beimaged, and the sensitivity of the imaging element. Even when differentwavelengths are chosen, a design solution that takes both diffractionefficiency and correction of chromatic aberration into account can beattained with a design according to the method of the present invention.

Furthermore, in this example, the diffraction lens was arranged on theingoing plane of a refraction lens, but the same effect can of coursealso be attained if a diffraction lens is arranged on the outgoing planeof a lens.

Twelfth Embodiment

The following is an explanation of an imaging lens according to atwelfth embodiment of the present invention, with reference to theaccompanying drawings.

The image pickup device shown in FIG. 22 comprises an imaging lens 1801according to the present invention, a CCD element 1802, and a signalprocessing circuit 1803.

The combined refraction/diffraction lens 1801 projects the imaged objectonto the CCD element 1802. The CCD element 1802 converts the opticalimage into electric signals. The electric signals output from the CCDelement 1802 are processed into image data by the signal processingcircuit 1803.

A lens according to the eleventh embodiment of the present invention isused for the combined refraction/diffraction lens. Therefore, thediffraction efficiency is high, even when the chromatic aberration iseliminated with the diffraction lens, and an image output with littleflare can be obtained.

Thirteenth Embodiment

In a lens with diffraction element, the radii of relief rings aredetermined by calculating positions at which the phase differences areshifted by an integer multiple of 2π (or at which the light path lengthsare shifted by an integer multiple of the wavelength) between adjacentrings. In this way, when a plane wave enters the lens with diffractionelement, the emergent ray from the lens forms a stairs-like wave frontwith phases shifting by 2π, but a new phase front is formed by adjacentrelief rings and is propagated as a wave having uniform phases. Theradii of the relief rings are determined by

r_(m)={square root over (2mλ₁f_(d))},  (24)

where r_(m) are the radii of the relief rings, m are the numbers of therings counted from the center of the lens, λ₁ is the principalwavelength of the diffraction element, and f_(d) is the focal length ofthe grating element.

A lens with a grating element of the thirteenth embodiment in accordancewith the present invention is described referring to the drawings in thefollowing.

FIG. 23 is a cross sectional view showing the configuration of the lenswith a grating element of the thirteenth embodiment. FIG. 24 is a graphshowing the relationship between the ray height and the phase delay ofthe lens with a grating element of the thirteenth embodiment. FIG. 25illustrates a specific relief profile of the diffraction element: FIG.25(a) is a schematic diagram showing the relief profile of thediffraction element determined by the above Equation (24), and FIG.25(b) is a schematic diagram showing the relief profile of thediffraction element of this embodiment.

FIG. 23 shows the lens with a grating element of this embodiment, inwhich a lens 3001 with grating element, a plate 3002 that is opticallyequal to a face plate in a crystal filter or an image pickup deviceetc., and an image surface 3005 are arranged in this order from theobject side (left side in the drawing).

In the relief formed on the grating element surface of the lens 3001with grating element of the thirteenth embodiment in accordance with thepresent invention, the pitches P_(m) of the relief satisfy theabove-mentioned Equation (7),${P_{m} > \sqrt{\frac{\lambda_{1} \cdot f_{d}}{2m}}},$

Where m is the ring number counted from the center of the lens, f_(d) isthe focal length of the grating element, and λ₁ is the principalwavelength when the grating element is formed. When Equation (7) issatisfied, the curve showing the relationship between the ray height andthe phase delay is present in the range as shown in FIG. 24.

When the Equation (7) is met, the relief profile of the diffractionelement can be a specific shape as shown in FIG. 25(b), where the reliefhas larger pitches, and have greatly reduced number of rings compared toa relief profile in the case of$P_{m} = \sqrt{\frac{\lambda_{1} \cdot f_{d}}{2m}}$

as shown in FIG. 25(a). As a result, formation of the grating elementsurface becomes easy, and decreased diffraction efficiency can beprevented, so that influence of unnecessary scattered light thatreflects in an image surface to decrease the imaging performance can beinhibited. If Equation (7) is not satisfied, the number of relief ringsis increased, and moreover, the pitches of the relief become smaller,resulting in decreased diffraction efficiency as well as processingdifficulties.

Furthermore, the grating element surface preferably has a kinoformprofile as shown in FIG. 25, and the lens with a grating element isproduced either by glass molding or plastic molding. In this way, a lenswith a grating element having a kinoform profile with excellenttranscription performance can be achieved.

Furthermore, the lens with a grating element may be made from aninfrared absorbing material. By using such a material, influence ofunnecessary light in the infrared spectrum generated by the gratingelement surface being projected on an image pickup device to decreasethe imaging performance can be inhibited, so that good imagingperformance can be maintained.

Fourteenth Embodiment

Next, a lens with a grating element of the fourteenth embodiment inaccordance with the present invention will be described referring to thedrawings.

FIG. 26 is a cross sectional view showing the configuration of the lenswith a grating element of the fourteenth embodiment, and FIG. 27illustrates a graph showing the relationship between the ray height andthe phase delay of the lens with a grating element of the fourteenthembodiment and a schematic diagram of a specific relief profile of adiffraction element, which is formed from the graph.

FIG. 26 shows the lens with a grating element of this embodiment, inwhich a lens 3001 with grating element, a plate 3002 that is opticallyequal to a face plate in a crystal filter or an image pickup deviceetc., and an image surface 3005 are arranged in this order from theobject side (left side in the drawing).

The shape of the relief formed on the grating element surface of thelens 3001 is derived from the curve showing the relationship between theray height and the phase delay in FIG. 27, and the relief rings arelocated at where the phase delay is an integer multiple of 2π. That is,the pitches of the relief gradually decrease up to a certain positionaway from the optical axis, and gradually increase further away fromthis position.

In such a configuration, the pitches of the relief at the periphery ofthe lens can be increased, so that a lens with a grating element whichcan easily be processed may be achieved. Also, because the pitches ofthe relief at the periphery of the lens can be increased, decrease indiffraction efficiency can be inhibited. As a result, influence ofunnecessary scattered light being projected on an image surface todecrease the imaging performance can be inhibited.

Furthermore, the grating element surface preferably has a kinoformprofile as shown in FIG. 27, and the lens with a grating element surfaceis preferably produced either by glass molding or plastic molding. Inthis way, a lens with a grating element having a kinoform profile withexcellent transcription performance can be achieved.

Furthermore, the lens with a grating element may be made from aninfrared absorbing material. By using such a material, influence ofunnecessary light in the infrared spectrum generated by the gratingelement surface being projected on an image pickup device to decreasethe imaging performance can be inhibited, so that good imagingperformance can be maintained.

Fifteenth Embodiment

Next, a lens with a grating element of the fifteenth embodiment inaccordance with the present invention will be described referring to thedrawings.

FIG. 28 is a cross sectional view showing the configuration of the lenswith a grating element of the fifteenth embodiment. FIG. 29 illustratesa graph showing the relationship between the ray height and the phasedelay of the lens with a grating element of the fifteenth embodiment,and a schematic diagram showing a specific relief profile of adiffraction element, which is made from the graph.

In FIG. 28, the lens with a grating element of this embodiment comprisesa lens 3001 with grating element, a plate 3002 optically equal to a faceplate in a crystal filter or an image pickup device etc., and an imagesurface 3005, which are arranged in this order from the object side(left side in the drawing). The shape of the relief formed on thegrating element surface of the lens 3001 is lead from the curve showingthe relationship between the ray height and the phase delay in FIG. 29.The lens 3001 with grating element of the fifteenth embodiment satisfiesthe above Equation (8), where r is the effective radius of the gratingelement surface, and d is the distance of the innermost ring of therelief from the optical axis.

By satisfying the Equation (8), the shape of the lens can beparticularly effective in correcting lateral chromatic aberration(magnification chromatic aberration), and it is particularly effectivein the case of a wide-angle lens having a field angle of at least 60°.That is, in a lens with diffraction element formed by satisfyingEquation (8), as is shown in FIG. 30, if an axial ray enters, thediameter of luminous flux hardly includes the relief rings on thediffraction element surface, so that the diffractive effect is small andthus the effect of correcting longitudinal chromatic aberration (axialchromatic aberration) is not obtained. On the other hand, if an abaxialray enters, a sufficient number of the relief rings are included in thediameter of luminous flux, so that the diffractive effect is large andthus the lateral chromatic aberration can be corrected effectively.

If the upper limit of the above-mentioned equation is exceeded, lateralchromatic aberration cannot be corrected sufficiently. If the lowerlimit of the equation is exceeded, excess correction of longitudinalchromatic aberration may result in order to correct lateral chromaticaberration sufficiently, so that good imaging performance cannot beobtained. In addition, the number of the relief rings also increases,resulting in decrease in diffraction efficiency.

Furthermore, the grating element surface preferably has a kinoformprofile as shown in FIG. 29, and the lens having the grating elementsurface is preferably produced either by glass molding or plasticmolding. In this way, a lens with a grating element having a kinoformprofile with excellent transcription performance can be achieved.

Furthermore, the above-mentioned lens with a grating element may be madefrom an infrared absorbing material. By using such a material, influenceof unnecessary light in the infrared spectrum generated by the gratingelement surface being projected on an image pickup device to decreasethe imaging performance can be inhibited, so that good imagingperformance can be maintained.

Sixteenth Embodiment

Next, the configuration of an imaging apparatus of the sixteenthembodiment of the present invention will be described referring to thedrawings.

The imaging apparatus shown in FIG. 31 comprises a lens 3001 withgrating element in accordance with the present invention, an imagepickup device 3011 and a signal processing circuit 3012. The numeral3013 designates an optical axis.

As the lens with a grating element, one of the thirteenth to fifteenthembodiments in accordance with the present invention is used. The lenseswith grating element of these embodiments in accordance with the presentinvention have a small size and are easily produced, and are thussuitable for making a very low-priced, small size imaging apparatus.

Thus, by making an imaging apparatus using the lens with a gratingelement of the present invention, the size of the entire apparatus canbe made smaller than a conventional apparatus, and a very low-priced,small size imaging apparatus having a good imaging performance can alsobe obtained.

Seventeenth Embodiment

Next, the configuration of a reading apparatus of the seventeenthembodiment of the present invention will be described referring to thedrawings.

The reading apparatus shown in FIG. 32 comprises a lens 3001 withgrating element in accordance with the present invention, an imagesensor 3021, and a signal processing circuit 3022. The numeral 3013refers to an optical axis.

As the lens with a grating element, one of the thirteenth to fifteenthembodiments in accordance with the present invention is used. In thelenses with grating element of these embodiments in accordance with thepresent invention, chromatic aberration is excellently corrected over awide range of wavelength. In addition, these lenses have a large fieldangle and also have a smaller size than a conventional optical system,thus being suitable for constituting a small size reading apparatus.

Accordingly, by constituting a reading apparatus using the lens with agrating element of the present invention, the size of the entire readingapparatus can be smaller than that of a conventional apparatus, and avery low-priced reading apparatus having a good imaging performance canalso be obtained.

Second Invention

The second invention will be further described in detail referring tothe following embodiments. First, a method of designing a gratingelement of the present invention will be described.

A grating element is an optical element utilizing the phenomenon ofdiffraction. While a refraction element has a high refractive index forshort wavelengths, the grating element has a higher diffractive anglefor longer wavelengths. Therefore, the effect of the grating element forchromatic aberration becomes opposite to that of a refraction element.The dispersion of the grating element is determined depending on theband of the wavelength used, and generally, in the case of color images,the band of the wavelength required for photographing is in the range ofabout 430 nm to 630 nm. In this range, the dispersion of the gratingelement becomes negative. When this grating element is combined with arefraction element having a positive refractive power, then achromatismcan be achieved by using a grating element having a positive refractivepower.

We used the high refractive index method proposed by William C.

Sweatt (see “Describing Holographic Optical Elements as Lenses”, Journalof Optical Society of America, Vol. 67, No. 6, June 1977) as a specificmethod for designing the grating element. The method indicates that theeffect of a grating element to a light ray can be displaced byrefraction of a hypothetical high refractive index, and when therefractive index becomes infinite, the refraction element completelycorresponds to the grating element. However, because an infiniterefractive index cannot be defined in actual designing, it must be setto a certain value. In the following, the error between the highrefractive index method and the actual diffractive grating will beexplained.

FIGS. 40 and 41 show the error analysis of the Sweatt's model. Thediffraction (see FIG. 40) can be found using the equation

n₁sinθ₁−n₂sinθ₂=λ/d.  (25)

On the other hand, because the refraction (see FIG. 41) takes placetwice, at a first surface and at a second surface, Snell's law appliestwice. The first application of Snell's law is expressed by the equation

n₁sinθ₁=n_(h)sinθ_(h),  (26)

and the second application of Snell's law is expressed by the equation

n_(h)sin(θ_(h)+φ_(h))=n₂sinθ₂.  (27)

If we suppose θ_(h)<<1, then the difference between the two outgoingradiation angles becomes λ/dn_(h) according to the above equations (25)to (27). The error Δ of the ray position on the image surface isexpressed by the equation

Δ=λ·f/d·n_(h),  (28)

where f is the focal length of the lens.

According to this equation, if the wavelength is 550 nm, the focallength f=5 mm, the pitch of the grating is 20 μm, and the highrefractive index n_(h)=5501, the error Δ of the ray position on theimage surface becomes Δ=0.025 μm. This is less than one tenths of thevalue that should be considered in designing, and thus it is of noproblem. Thus, in the case of designing by the high refractive indexmethod, the refractive index was set ten times the wavelength plus one.One is added because if a first order diffracted light is used, thepitch of the grating is determined at every height of λ/(n−1). That is,if the refractive index n=10λ+1, the pitches may be etched at every 0.1nm. This is convenient because the number of grating rings can bedetermined readily by calculating the sag of the high refractive indexlayer. For example, if the sag of the high refractive index layer is 2.5nm, the number of grating rings is 25. However, for the actual number ofgrating rings, the refracted direction of the ray also has to beconsidered, so the number of grating rings cannot be calculatedcorrectly, if only the sag measured vertically to the surface isconsidered, but it is useful for approximation.

Eighteenth Embodiment

In the following, an optical system for reading of the eighteenthembodiment in accordance with the present invention will be describedreferring to FIGS. 33 and 35.

FIGS. 33 and 35 are cross sectional views showing the configuration ofthe lenses in the optical system for reading of the Examples 14 and 15respectively, which are specific numerical examples of the eighteenthembodiment.

As shown in FIGS. 33 and 35, the optical system for reading according tothis embodiment comprises a diaphragm 5001, a lens 5002, and a flatplate 5003 that is optically equal to a face plate in an image pickupdevice, which are arranged in this order from the object side (left sidein the drawing). The numeral 5004 designates an image surface in FIGS.33 and 35.

The lens 5002 constituting this optical system for reading has a conveximage side surface, and a grating element surface 5060 having a positiverefractive power is formed on the image side surface. In addition, theobject side surface of the lens 5002 is an aspheric surface with a localradius of curvature that becomes smaller with increasing distance fromthe optical axis.

The numerical values shown for the image side surface of the lens 5002in the later described examples are the values before conversion intothe grating element surface 5060, and the grating element surface 5060is formed based on these numerical values. To be specific, at the timeof design, as shown in FIG. 42, it is assumed that the image sidesurface has a base aspheric surface 5050 (the third surface having aradius r₃ of curvature at the vertex in Examples 14 and 15), a highrefractive index surface 5051 (the second surface having a radius r₂ ofcurvature at the vertex in Examples 14 and 15) located on the basesurface, and a high refractive index portion 5052 between the twosurfaces. Then, in order to obtain the same effects as this image sidesurface comprising the base aspheric surface 5050 and the highrefractive index surface 5051, they are converted to the grating elementsurface 5060 as shown in FIG. 43 by the above-mentioned method.

The grating element surface 5060 has a kinoform profile as shown in FIG.44, and the lens 5002 having the grating element surface 5060 is formedeither by glass molding or plastic molding. Thus, an optical system forreading having a kinoform profile with excellent transcriptionperformance can be achieved.

Furthermore, by making the lens 5002 having the grating element surface5060 from an infrared absorbing material such as an infrared rayinsulating glass etc., an optical system for reading having a kinoformprofile with excellent transcription performance, in which unnecessarylight in the infrared spectrum generated by the grating element surface5060 is prevented from being projected on an image sensor to decreasethe imaging performance, and thus ensuring good imaging performance, canbe achieved.

In this embodiment, the following effects can be obtained by satisfyingthe equations

0.05<|r₂/r₁|<0.5,  (9)

9<f/D<16,  (10)

and

0.05<|f/f_(d)|<0.15,  (11)

where r₁ is the radius of curvature at the vertex of the object sidesurface of the lens 5002 (the first surface), r₂ is the radius ofcurvature at the vertex of the image side surface, D is the diameter ofthe diaphragm 5001, f is the focal length of the entire optical system,and f_(d) is the focal length of the grating element surface 5060.

First, by satisfying Equation (9) above, an optimal lens shape inbalance of all the aberrations can be obtained. If it does not fall inthe range of Equation (9), the incident angle of an abaxial ray isincreased, and as a result, abaxial performance or diffractionefficiency to an abaxial ray decreases, and flare is generated.Moreover, if the radius r₂ of curvature at the vertex of the image sidesurface becomes small, lens production becomes more difficult, and thismay become a factor in decreasing yield and rising cost.

Then, by satisfying Equation (10) above, sufficient depth of field toprevent loss of image information or erroneous recognition of codeinformation due to vibration etc. can be obtained. If it does not fallin the range of Equation (10), sufficient brightness for reading imageinformation or code information may not be obtained, or sufficient depthof field may not be obtained, thus causing loss of image information orerroneous recognition of code information.

Then, by satisfying Equation (11) above, chromatic aberration can beexcellently corrected. If it does not fall in the range of Equation(11), chromatic aberration is not corrected sufficiently, or iscorrected excessively, so that good imaging performance is difficult toobtain.

Furthermore, as mentioned above, by providing at least one surface ofthe lens 5002 with an aspheric shape with local radius of curvature thatbecomes smaller with increasing distance from the optical axis,distortion aberration and curvature of field can be correctedeffectively.

Furthermore, unnecessary scattered light generated by the gratingelement surface 5060 can be prevented from being projected on an imagesensor so as to decrease the image performance by satisfying theequation

450 nm<λ₁<600 nm,  (12)

where λ₁ is the principal wavelength when the grating element surface5060 is formed.

If it does not fall in the range of Equation (12), unnecessary scatteredlight becomes strong to the sensitivity for wavelength of the imagesensor, and flare is generated.

Furthermore, in the optical system for reading, miniaturization of theoptical system for reading can be achieved by satisfying the Equation

0.2<y/Y<0.6,  (13)

where Y is the maximum height of a manuscript and y is the maximumheight of an image sensor.

However, if it does not fall in the range of Equation (13), the distancebetween the object and the image increases. In addition, distortionaberration and curvature of field are deteriorated, so that good imagingperformance cannot be obtained, or only a part of a desired reading sizeof a manuscript can be read, so that operation and response performancesare deteriorated.

Furthermore, by making the meridional image surface to have a betterimaging performance than the sagittal image surface in the opticalsystem for reading, the precision of the reading code information can beenhanced, so that erroneous recognition can be prevented.

In the following, Examples 14 and 15 are given as specific numericalexamples of this embodiment. In these Examples, f is the total focallength of the entire system, F_(no) is the f number, and 2ω is the fieldangle. In these Examples, r₁, r₂ and r₃ designate the radius ofcurvature at the vertex of the object side lens surface (the firstsurface), the radius of curvature at the vertex of the high refractiveindex surface of the image side surface (the second surface), and theradius of curvature at the vertex of the base aspheric surface of theimage side surface (the third surface), respectively; d₁, d₂ and d₃represent the distance between the diaphragm 5001 and the first surfaceof the lens 5002, the distance between the first surface and the secondsurface (the thickness of the lens), and the distance between the secondsurface and the third surface, respectively; and n and ν are therefractive index and the Abbe number of the lens material for d-rayrespectively. The surface having an aspheric shape (marked with anasterisk ⋆ in the column “Surface No.” in the Examples) is ruled by thefollowing equation $\begin{matrix}{{Z = {\frac{{cy}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}y^{2}}}} + {Dy}^{4} + {Ey}^{6} + {Fy}^{8} + {Gy}^{10}}},} & (29)\end{matrix}$

with

Z: The sag at the height y from the optical axis

y: Height from the optical axis

c: Curvature at the vertex of an aspheric surface

k: Conical constant

D, E, F and G: Aspheric coefficients.

In the following, specific numerical values of Example 14 are given. Inthis Example, the high refractive surfaces that have been designed bythe high refractive index method are marked with a circle (◯) in thecolumn “Surface No.”

EXAMPLE 14

f=24.4

F_(no)=15.2, 2ω=50.0

Y=25.0, y=10.5

Surface No. r d n ν Diaphragm d₁ = 0.5 1 ⋆ r₁ = −13.2300 d₂ = 5.0 1.524056.7 2 ⋆ ◯ r₂ = −7.60302 d₃ = 0.0 5877 −3.45 3 ⋆ r₃ = −7.60300

The surfaces marked with ⋆ are aspheric surfaces, and the asphericcoefficients thereof are given below.

First Surface Second Surface Third Surface k 0.0 0.0 0.0 D −1.23566 ×10⁻³   1.17662 × 10⁻⁴   1.17649 × 10⁻⁴ E   6.16012 × 10⁻⁴ −1.94690 ×10⁻⁶ −1.94714 × 10⁻⁶ F 0.0 0.0 0.0 G 0.0 0.0 0.0

FIG. 34 shows the aberrations in an optical system for reading accordingto the above Example 14.

In FIGS. 34, (a), (b), (c), (d) and (e) denote spherical aberration(mm), astigmatism (mm), distortion aberration (%), longitudinalchromatic aberration (mm), and lateral chromatic aberration (mm),respectively. In FIG. 34(a), which shows spherical aberration, the solidline is the value for d-ray, and the broken line is the sine condition.In FIG. 34(b), which shows astigmatism, the solid line is the curvatureof the sagittal image surface, and the broken line is the curvature ofthe meridional image surface. In FIG. 34(d), which shows longitudinalchromatic aberration, the solid line is the values for d-ray, the brokenline is the value for F-ray, and the alternate long and short dash lineis the value for C-ray. In FIG. 34(e), which shows lateral chromaticaberration, the broken line is the value for F-ray, and the alternatelong and short dash line is the value for C-ray. As is evident fromthese diagrams, according to this Example, chromatic aberration isexcellently corrected and an optical system for reading that displaysgood imaging performance can be attained.

In the following, specific numerical values are given for Example 15.

EXAMPLE 15

f=17.0

F_(no)=10.4, 2ω=56.5

Y=32.5, y=10.5

Surface No. r d n ν Diaphragm d₁ = 2.8 1 ⋆ r₁ = −11.5083 d₂ = 2.6 1.529855.7 2 ⋆ ◯ r₂ = −5.63147 d₃ = 0.0 5877 −3.45 3 ⋆ r₃ = −5.63145

The surfaces marked with ⋆ are aspheric surfaces, and the asphericcoefficients thereof are given below.

First Surface Second Surface Third Surface k 0.0 0.0 0.0 D −2.01753 ×10⁻³   −1.35383 × 10⁻⁴ −1.35410 × 10⁻⁴ E 5.50497 × 10⁻⁴ −8.57270 × 10⁻⁶−8.57284 × 10⁻⁶ F −1.17212 × 10⁻⁴   −2.27625 × 10⁻⁷ −2.27024 × 10⁻⁷ G5.67473 × 10⁻⁶ −1.49093 × 10⁻⁷ −1.49150 × 10⁻⁷

FIG. 36 shows the aberrations in an optical system for reading accordingto Example 15.

In FIGS. 36, (a), (b), (c), (d) and (e) denote spherical aberration(mm), astigmatism (mm), distortion aberration (%), longitudinalchromatic aberration (mm), and lateral chromatic aberration (mm),respectively. In FIG. 36(a), which shows spherical aberration, the solidline is the value for d-ray, and the broken line is the sine condition.In FIG. 36(b), which shows astigmatism, the solid line is the curvatureof the sagittal image surface, and the broken line is the curvature ofthe meridional image surface. In FIG. 36(d), which shows longitudinalchromatic aberration, the solid line is the value for d-ray, the brokenline is the value for F-ray, and the alternate long and short dash lineis the value for C-ray. In FIG. 36(e), which shows lateral chromaticaberration, the broken line is the value for F-ray, and the alternatelong and short dash line is the value for C-ray. As is evident fromthese diagrams, according to this Example, chromatic aberration isexcellently corrected and an optical system for reading that displaysgood imaging performance can be attained.

Having described an optical system for reading in which a gratingelement surface is formed on the image side surface of the lens 5002 asan example in this embodiment, the present invention is not limited tothis configuration, and the grating element surface may be formed on theobject side surface of the lens 5002.

Nineteenth Embodiment

In the following, an optical system for reading of the nineteenthembodiment in accordance with the present invention will be describedreferring to FIG. 37.

FIGS. 37 is a cross sectional view showing the configuration of the lensin the optical system for reading of Example 16, which is a specificnumerical example of the nineteenth embodiment.

As shown in FIG. 37, the optical system for reading according to thisembodiment comprises a diaphragm 5001, a lens 5002, and a plate 5003optically equal to a face plate in an image pickup device, which arearranged in this order from the object side (left side in the drawing),and it can read manuscripts of different sizes as it is moved on theoptical axis by a driving device not shown in the drawing. The numeral5004 designates an image surface in FIG. 37.

The lens 5002 constituting this optical system for reading has a conveximage side surface, and also is an aspheric surface with a local radiusof curvature that becomes smaller with increasing distance from theoptical axis. In addition, in the lens 5002, a grating element surface5060 having a positive refractive power is formed on the image sidesurface.

The numerical values shown for the image side surface of the lens 5002as described later in Example 16 are the values before conversion intothe grating element surface 5060, and the grating element surface 5060is formed based on these numerical values. To be specific, at the timeof designing, as shown in FIG. 42, it is assumed that the image sidesurface has a base aspheric surface 5050 (the third surface having aradius r₃ of curvature at the vertex in Example 16), a high refractiveindex surface 5051 (the second surface having a radius r₂ of curvatureat the vertex in Example 16) located on the base surface, and a highrefractive index portion 5052 between the two surfaces. Then, in orderto obtain the same effects as this image side surface comprising thebase aspheric surface 5050 and the high refractive index surface 5051,they are converted to the grating element surface 5060 as shown in FIG.43 by the above-mentioned method.

The grating element surface 5060 has a kinoform profile as shown in FIG.44, and the lens 5002 having the grating element surface 5060 is formedeither by glass molding or plastic molding. Thus, an optical system forreading having a kinoform profile with excellent transcriptionperformance can be achieved.

Furthermore, by making the lens 5002 having the grating element surface5060 from an infrared absorbing material, an optical system for readinghaving a kinoform profile with excellent transcription performance, inwhich unnecessary scattered light generated by the grating elementsurface 5060 is prevented from being projected on an image sensor todecrease the imaging performance, and thus ensuring good imagingperformance, can be achieved.

In this embodiment, the following effects can be obtained by satisfyingthe equations

0.05<|r₂/r₁|<0.5,  (9)

9<f/D<16,  (10)

and

0.05<|f/f_(d)|<0.15,  (11)

where r₁ is the radius of curvature at the vertex of the object sidesurface of the lens 5002 (the first surface), r₂ is the radius ofcurvature at the vertex of he image side surface, D is the diameter ofthe diaphragm 5001, f is the focal length of the entire optical system,and f_(d) is the focal length of the grating element surface 5060.

First, by satisfying Equation (9) above, an optimal lens shape inbalance of various aberrations can be obtained. However, if it does notfall in the range of Equation (9), the incident angle of an abaxial rayis increased, and as a result, abaxial performance or diffractionefficiency to an abaxial ray decreases, and flare is generated.Furthermore, if the radius r₂ of curvature at the vertex of the imageside surface is small, lens production becomes difficult, so that yieldis decreased and also production cost is increased.

Then, by satisfying Equation (10) above, sufficient depth of field so asto prevent loss of image information or erroneous recognition of codeinformation due to vibration etc. can be obtained. However, if it doesnot fall in the range of Equation (10), sufficient brightness forreading image information or code information may not be obtained, orsufficient depth of field may not be obtained, causing loss of imageinformation or erroneous recognition of code information.

Then, by satisfying Equation (11) above, chromatic aberration can beexcellently corrected. If it does not fall in the range of Equation(11), chromatic aberration is not corrected sufficiently or is correctedexcessively, so that good imaging performance is difficult to obtain.

Furthermore, as mentioned above, by making at least one surface of thelens 5002 to be an aspheric shape with a local radius of curvature thatbecomes smaller with increasing distance from the optical axis,distortion aberration and curvature of field can be correctedeffectively.

Furthermore, unnecessary scattered light generated by the gratingelement surface 5060 can be prevented from being projected on an imagesensor so as to decrease the image performance by satisfying theequation

450 nm<λ₁<600 nm,  (12)

where λ₁ is the principal wavelength when the grating element surface5060 is formed.

If it does not fall in the range of Equation (12), unnecessary scatteredlight becomes too strong to the sensitivity for wavelength of the imagesensor, and flare is generated.

Furthermore, in the optical system for reading, miniaturization of theoptical system for reading can be achieved by satisfying the equation

0.2<y/Y<0.6,  (13)

where Y is the maximum height of a manuscript and y is the maximumheight of an image sensor.

If it does not fall in the range of Equation (13), the distance betweenthe object and the image increases. In addition, distortion aberrationand curvature of field are deteriorated so that good imaging performancecannot be obtained, or only a part of a desired reading size ofmanuscript can be read, so that operation and response performances aredeteriorated.

Furthermore, in the optical system for reading, a small size opticalsystem for reading having a good imaging performance can be achieved bysatisfying the equation

0.6<Y_(t)/Y_(W)<1,  (14)

where Y_(W) is the maximum height of a manuscript when the opticalsystem for reading is moved closest to the object side, and Y_(t) is themaximum height of a manuscript when the optical system for reading ismoved closest to the image side.

If it does not fall in the range of Equation (14), the amount ofmovement of the lens increases, so that miniaturization of the apparatuscannot be attained, and also a good imaging performance cannot beobtained.

Furthermore, by making the meridional image surface have better imagingperformance than the sagittal image surface in the optical system forreading, precision of reading code information can be enhanced, so thaterroneous recognition can be prevented.

In the following, Examples 16 is given as a specific numerical exampleof this embodiment. In this Example, f is the total focal length of theentire system, F_(no) is the f number, and 2ω is the field angle. Inthis Example, r₁, r₂ and r₃ designate the radius of curvature at thevertex of the object side lens surface (the first surface), the radiusof curvature at the vertex of the high refractive index surface of theimage side surface (the second surface), and the radius of curvature atthe vertex of the base aspheric surface of the image side surface (thethird surface), respectively; d₁, d₂ and d₃ represent the distancebetween the diaphragm 5001 and the first surface of the lens 5002, thedistance between the first surface and the second surface (the thicknessof the lens), and the distance between the second surface and the thirdsurface, respectively; and n and ν are the refractive index and the Abbenumber of the lens material for d-ray, respectively. The surface havingan aspheric shape (marked with an asterisk ⋆ in the column “Surface No.”in the Example) is ruled by the following equation $\begin{matrix}{{Z = {\frac{{cy}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}y^{2}}}} + {Dy}^{4} + {Ey}^{6} + {Fy}^{8} + {Gy}^{10}}},} & (29)\end{matrix}$

with

Z: The sag at the height y from the optical axis

y: Height from the optical axis

c: Curvature at the vertex of an aspheric surface

k: Conical constant

D, E, F and G: Aspheric coefficients.

In the following, specific numerical values of Example 16 are given.

In this Example, the high refractive surfaces that have been designed bythe high refractive index method are marked with a circle (◯) in thecolumn “Surface No.”

EXAMPLE 16

f=17.2

F_(no)=10.4, 2ω=55.4 to 52.7

Surface No. r d n ν Position of Manuscript (variable) Diaphragm d₁ = 2.81 ⋆ r₁ = −11.6748 d₂ = 2.6 1.5298 55.7 2 ⋆ ◯ r₂ = −5.71453 d₃ = 0.0 5877−3.45 3 ⋆ r₃ = −5.71451 d Yw = 25.0 51.0 Yt = 32.5 62.4

The surfaces marked with ⋆ are aspheric surfaces, and the asphericcoefficients thereof are given below.

First Surface Second Surface Third Surface k 0.0 0.0 0.0 D −2.06110 ×10⁻³ −1.29557 × 10⁻⁴ −1.29590 × 10⁻⁴ E   5.32089 × 10⁻⁴ −7.96984 × 10⁻⁶−7.96763 × 10⁻⁶ F −1.22456 × 10⁻⁴ −2.04872 × 10⁻⁷ −2.04907 × 10⁻⁷ G  8.67146 × 10⁻⁶ −1.30728 × 10⁻⁷ −1.30735 × 10⁻⁷

FIGS. 38 and 39 show the aberrations in an optical system for readingaccording to this Example 16.

FIG. 38 shows drawings of the aberrations when the optical system forreading is moved closest to the object side, and FIG. 39 shows drawingsof the aberrations when the optical system for reading is moved closestto the image side. In FIGS. 38 and 39, (a), (b), (c), (d) and (e) denotespherical aberration (mm), astigmatism (mm), distortion aberration (%),longitudinal chromatic aberration (mm), and lateral chromatic aberration(mm) respectively. In the FIG. 38(a) and FIG. 39(a), each of which showsspherical aberration, the solid line is the value for d-ray, and thebroken line is the sine condition. In the FIG. 38(b) and FIG. 39(b),each of which shows astigmatism, the solid line is the curvature of thesagittal image surface, and the broken line is the curvature of themeridional image surface. In FIG. 38(d) and FIG. 39(d), each of whichshows longitudinal chromatic aberration, the solid line is the value ford-ray, the broken line is the value for F-ray, and the alternate longand short dash line is the value for C-ray. In FIG. 38(e) and FIG.39(e), each of which shows lateral chromatic aberration, the broken lineis the value for F-ray, and the alternate long and short dash line isthe value for C-ray. As is evident from these diagrams, according tothis Example, chromatic aberration is excellently corrected and anoptical system for reading that displays good imaging performance can beattained.

Having described an optical system for reading in which a gratingelement surface is formed on the image side surface of the lens 5002 asan example in this embodiment, the present invention is not limited tothis configuration, and the grating element surface may be formed on theobject side surface of the lens 5002.

Twentieth Embodiment

Next, an image reading apparatus of the twentieth embodiment inaccordance with the present invention will be described referring toFIG. 45.

FIG. 45 is a schematic diagram showing an image reading apparatus of thetwelfth embodiment in accordance with the present invention.

As shown in FIG. 45, the image reading apparatus comprises an opticalsystem for reading 5061, an image sensor 5062 for converting the imageinformation imaged by the optical system for reading 5061 into electricsignals, and a circuit portion 5063 for processing the electric signalsto process the image information etc.

The optical system for reading of the above eighteenth embodiment isused as the optical system for reading 5061. In the optical system forreading of the eighteenth embodiment, chromatic aberration isexcellently corrected over a wide range of wavelength, and the fieldangle is large, and in addition it is smaller than a conventionaloptical system, so that it is suitable for constituting a small sizeimage reading apparatus.

Accordingly, by constituting an image reading apparatus using theoptical system for reading of the above eighteenth embodiment, the sizeof the entire image reading apparatus can be smaller than that of aconventional apparatus, and also an image reading apparatus having agood imaging performance can be obtained.

Twenty-first Embodiment

Next, an image reading apparatus of the twenty-first embodiment inaccordance with the present invention will be described referring toFIG. 46.

FIG. 46 is a schematic diagram showing an image reading apparatus of thetwenty-first embodiment in accordance with the present invention.

As shown in FIG. 46, the image reading apparatus comprises an opticalsystem for reading 5071, a driving device 5072 for driving the opticalsystem for reading 5071, and an image sensor 5062 for converting theimage information imaged by the optical system for reading 5071 intoelectric signals, and a circuit portion 5063 for processing the electricsignals to process the image information etc.

The optical system for reading of the above nineteenth embodiment isused as the optical system for reading 5071. In the optical system forreading of the nineteenth embodiment, chromatic aberration isexcellently corrected over a wide range of wavelength, the field angleis large, and also it is smaller than a conventional optical system, sothat it is suitable for constituting a small size image readingapparatus.

Accordingly, by constituting an image reading apparatus using theoptical system for reading of the above nineteenth embodiment, the sizeof the entire image reading apparatus can be made smaller than that of aconventional apparatus, and also an image reading apparatus having agood imaging performance can be obtained.

Twenty-second Embodiment

Next, a bar code reader of the twenty-second embodiment in accordancewith the present invention will be described referring to FIG. 47.

FIG. 47 is a schematic diagram showing a bar code reader of thetwenty-second embodiment in accordance with the present invention.

As shown in FIG. 47, the bar code reader comprises an optical system forreading 5061, an image sensor 5073 for converting the bar codeinformation imaged by the optical system for reading 5061 into electricsignals, and a signal processing circuit 5074 having a circuit portionfor decoding the bar code information etc.

The optical system for reading of the above eighteenth embodiment isused as the optical system for reading 5061. In the optical system forreading of the above eighteenth embodiment, chromatic aberration isexcellently corrected over a wide range of wavelength, so that a lightsource such as LED is not required, and also the field angle is large,and in addition it is smaller than a conventional optical system, sothat it is suitable for constituting a small size bar code reader.

Accordingly, by constituting a bar code reader using the optical systemfor reading of the above the eighteenth embodiment, the size of theentire bar code reader can be smaller than that of a conventional one,and also a bar code reader having a good imaging performance can beobtained.

Twenty-third Embodiment

Next, a bar code reader of the twenty-third embodiment in accordancewith the present invention will be described referring to FIG. 48.

FIG. 48 is a schematic diagram showing a bar code reader of thetwenty-third embodiment in accordance with the present invention.

As shown in FIG. 48, the bar code reader comprises an optical system forreading 5071, a driving device 5072 for driving the optical system forreading 5071, an image sensor 5073 for converting the bar codeinformation imaged by the optical system for reading 5071 into electricsignals, and a signal processing circuit 5074 having a circuit portionfor decoding the bar code information etc.

The optical system for reading of the above nineteenth embodiment isused as the optical system for reading 5071. In the optical system forreading of the above nineteenth embodiment, chromatic aberration isexcellently corrected over a wide range of wavelength, so that a lightsource such as LED is not required, and also the field angle is large,and in addition it is smaller than a conventional optical system, sothat it is suitable for constituting a small size bar code reader.

Accordingly, by constituting a bar code reader using the optical systemfor reading of the above nineteenth embodiment, the size of the entirebar code reader can be made smaller than that of a conventional one, andalso a bar code reader having a good imaging performance can beobtained.

The invention may be embodied in other specific forms without departingfrom the spirit or essential characteristics thereof The embodimentsdisclosed in this application are to be considered in all respects asillustrative and not restrictive, the scope of the invention beingindicated by the appended claims rather than by the foregoingdescription, all changes that come within the meaning and range ofequivalency of the claims are intended to be embraced therein.

What is claimed is:
 1. A combined refraction/diffraction lens,comprising a refraction lens; and a diffraction lens comprising aplurality of concentric grating rings formed on at least one surface ofthe refraction lens; satisfying the formula $\begin{matrix}{{k = {f\left( {\frac{1}{f_{g}} + \frac{v_{g}}{f_{d}v_{d}}} \right)}},} & (6)\end{matrix}$

 wherein: f: total focal length of said combined refraction/diffractionlens f_(d): focal length of the diffraction lens f_(g): focal length ofthe refraction lens ν_(d): partial dispersion coefficient at an appliedwavelength region of the diffraction lens ν_(g): partial dispersioncoefficient at an applied wavelength region of the refraction lens wherein k satisfies 0.1≦k.
 2. The combined refraction/diffraction lensaccording to claim 1, wherein said k satisfies 0.2≦k≦0.8.
 3. A combinedrefraction/diffraction objective lens for use in an optical informationrecording/reproducing device, comprising: a single lens having aningoing surface and an outgoing surface; and a diffraction lenscomprising a plurality of concentric grating rings formed on at leastone surface of the single lens; satisfying the formula $\begin{matrix}{{k = {f\left( {\frac{1}{f_{g}} + \frac{v_{g}}{f_{d}v_{d}}} \right)}},} & (6)\end{matrix}$

 wherein: f: total focal length of said combined refraction diffractionobjective lens f_(d): focal length of the diffraction lens f_(g): focallength of the refraction lens ν_(d): partial dispersion coefficient atan applied wavelength region of the diffraction lens ν_(g): partialdispersion coefficient at an applied wavelength region of the refractionlens  wherein k satisfies 0.2≦k≦0.6.
 4. The combinedrefraction/diffraction objective lens according to claim 3, wherein saidk satisfies 0.3≦k≦0.55.
 5. An optical head comprising a light source; abeam splitting means for splitting a light beam emitted from said lightsource; a focussing means for focussing a light beam emitted from saidlight source on an information recording medium; a photo-detectorelement for detecting a light beam that is reflected or a transmitted bysaid information recording medium, wherein said focussing meanscomprises an objective lens according to claim 3 or claim
 4. 6. Acombined refraction/diffraction imaging lens comprising: a single lenshaving an ingoing surface and an outgoing surface; and a diffractionlens comprising a plurality of concentric grating rings formed on atleast one surface of the single lens; satisfying the formula$\begin{matrix}{{k = {f\left( {\frac{1}{f_{g}} + \frac{v_{g}}{f_{d}v_{d}}} \right)}},} & (6)\end{matrix}$

 wherein: f: total focal length of said combined refraction/diffractionimaging lens f_(d): focal length of the diffraction lens f_(g): focallength of the refraction lens ν_(d): partial dispersion coefficient atan applied wavelength region of the diffraction lens ν_(g): partialdispersion coefficient at an applied wavelength region of the refractionlens  wherein k satisfies 0.3≦k.
 7. The combined refraction/diffractionimaging lens according to claim 6, wherein said k satisfies 0.4≦k≦0.7.8. An image pickup device comprising an imaging lens according to claim6 or claim 7, an imaging element, and a signal processing circuit.
 9. Alens with grating element wherein chromatic aberration is corrected byforming concentric relief rings on a surface of the lens to providediffractive effect, the pitch P_(m) of the relief rings satisfying theformula $\begin{matrix}{{P_{m} > \sqrt{\frac{\lambda_{1} \cdot f_{d}}{2m}}},} & (7)\end{matrix}$

where m is the ring number counted from the center of the lens, f_(d) isthe focal length of the grating element, and λ₁ is the principalwavelength of the grating element.
 10. A lens with grating element inwhich chromatic aberration is corrected by forming concentric reliefrings on a surface of the lens to provide diffractive effect, satisfyingthe formula $\begin{matrix}{{0.2 < {\frac{d}{r}} < 0.7},} & (8)\end{matrix}$

where r is the effective radius of the grating element surface, and d isthe distance of the innermost ring of the relief from the optical axis.11. The lens with grating element according to claim 9 or 10, whereinthe surface of said grating element has a kinoform profile.
 12. The lenswith grating element according to claim 9 or 10, wherein said lens withgrating element is made of a material selected from the group consistingof glass and plastics.
 13. The lens with grating element according toclaim 9 or 10, wherein said lens with grating element is formed from aninfrared absorbing material.
 14. An imaging apparatus comprising atleast the lens with grating element according to claim 9 or 10, an imagesensor, and a signal processing circuit.
 15. A reading apparatuscomprising at least the lens with grating element according to claim 9or 10, an image sensor, and a signal processing circuit.
 16. An opticalsystem for reading optical information selected from the groupconsisting of image information and code information, comprising a lenswherein a grating element surface is formed on at least one surface ofthe lens, the optical system being suitable for being moved on anoptical axis by a driving device, wherein the lens which constitutes theoptical system for reading is only a single lens on which said gratingelement surface is formed, the image side surface of said lens is convexand has positive refractive power, and a diaphragm is placed at theobject side from said lens.
 17. The optical system for reading accordingto claim 16, which satisfies the formulas 0.05<|r₂/r₁|<0.5,  (9)9<f/D<16,  (10) and 0.05<|f/f_(d)|<0.15,  (11) where r₁ is the radius ofcurvature at the vertex of the object side surface of said lens, r₂ isthe radius of curvature at the vertex of the image side surface of saidlens, D is the diameter of the diaphragm, f is the focal length of theentire optical system, and f_(d) is the focal length of the gratingelement surface of said lens.
 18. The optical system for readingaccording to claim 16, wherein at least one surface of said lens is anaspheric surface with a local radius of curvature that becomes smallerwith increasing distance from the optical axis.
 19. The optical systemfor reading according to claim 16, which satisfies the formula 450nm<λ₁<600 nm,  (12) where λ₁ is the principal wavelength when thegrating element surface is formed.
 20. The optical system for readingaccording to claim 19, wherein the grating element surface has akinoform profile.
 21. The optical system for reading according to claim16, wherein the lens having the grating element surface is made of amaterial selected from the group consisting of glass and plastics. 22.The optical system for reading according to claim 16, wherein the lenshaving the grating element surface is formed from an infrared absorbingmaterial.
 23. The optical system for reading according to claim 16,which satisfies the formula 0.2<y/Y<0.6,  (13) where Y is the maximumheight of a manuscript, and y is the maximum height of an image sensor.24. The optical system for reading according to claim 23, wherein themeridional image surface has a better imaging performance than thesagittal image surface.
 25. An optical system for reading opticalinformation selected from the group consisting of image information andcode information, comprising a lens wherein a grating element surface isformed on at least one surface of the lens, the optical system beingsuitable for being moved on an optical axis by a driving device, whereinthe optical system satisfies the formula 0.6<Y_(t)/Y_(w)<1,  (14) whereY_(w) is the maximum height of a manuscript when the optical system ismoved closest to the object side, and Y_(t) is the maximum height of amanuscript when the optical system is moved closest to the image side.26. An image reading apparatus comprising the optical system for readingaccording to claim 16, an image sensor for converting image informationthat is imaged by said optical system for reading into electricalsignals, and a circuit portion for processing said electric signals toprocess said image information.
 27. A bar code reader comprising theoptical system for reading according to claim 16, an image sensor forconverting bar code information that is imaged by said optical systemfor reading into electric signals, and a signal processing circuithaving a circuit portion for decoding said bar code information.
 28. Adiffraction lens comprising a plurality of regions, each regioncomprising at least one grating ring, wherein the relief profile of thelens is optimized for particular desired lens properties and processingcharacteristics according to analysis of the diffraction efficiencies ofthe entire lens using the formula $\begin{matrix}{E_{j} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mj}}}} & (1)\end{matrix}$

wherein: j: integer indicating the order of diffraction light E_(j):diffraction efficiency for j-th order diffraction light of thediffraction lens M: positive integer (M>1) indicating the number ofregions for which the diffraction efficiency is calculated m: index ofthe region for which the diffraction efficiency is calculated η_(mj):diffraction efficiency for the j-th order diffraction light of the m-thregion W_(m): weight for the m-th region.
 29. A diffraction lenscomprising a plurality of regions, each region comprising at least onegrating ring, wherein the relief profile of the lens is optimized forparticular desired lens properties and processing characteristicsaccording to analysis of the diffraction efficiencies of the entire lensusing the formula $\begin{matrix}{E_{jl} = {\sum\limits_{m = 1}^{M}{W_{m}\eta_{mjl}}}} & (5)\end{matrix}$

wherein: j: integer indicating the order of diffraction light l: indexof the wavelengths E_(jl): diffraction efficiency for j-th orderdiffraction light of the diffraction lens at the l-th wavelength M:positive integer (M>1) indicating the number of regions for which thediffraction efficiency is calculated m: index of the region for whichthe diffraction efficiency is calculated W_(m): weight for the m-thregion η_(mjl): diffraction efficiency for the j-th order diffractionlight of the m-th region at the l-th wavelength.